In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers...

Jacobsthal is a surname. Notable people with the surname include: Ernst Jacobsthal (1882–1965), German mathematician Jacobsthal number, an integer sequence...

two 1349 = Stern-Jacobsthal number 1350 = nonagonal number 1351 = number of partitions of 28 into a prime number of parts 1352 = number of surface points...

in Trondheim. Jacobsthal sum Jacobsthal number Fermat's theorem on sums of two squares Selberg, Sigmund (2006-10-27). "Ernst Jacobsthal". Retrieved 2007-10-05...

Wagstaff prime with four digits, Jacobsthal prime 2736 – octahedral number 2741 – Sophie Germain prime, 400th prime number 2744 = 143, palindromic in base...

[and] seventy-one) is the natural number following 170 and preceding 172. 171 is a triangular number and a Jacobsthal number. There are 171 transitive relations...

the number 1 differently than larger numbers, sometimes even not as a number at all. Euclid, for example, defined a unit first and then a number as a...

mathematics, Jacobsthal sums are finite sums of Legendre symbols related to Gauss sums. They were introduced by Jacobsthal (1907). The Jacobsthal sum is given...

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has...

67280421310721} 65537 is also the 17th Jacobsthal–Lucas number, and currently the largest known integer n for which the number 10 n + 27 {\displaystyle 10^{n}+27}...

irregular prime, a prime that is one more than a square, and a Jacobsthal–Lucas number. Four-fold 257 is 1028, which is the prime index of the fifth Mersenne...

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that...

A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n ( n + 1 ) {\displaystyle n(n+1)} . The study...

In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci...

In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number...

A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are...

In mathematics, a double Mersenne number is a Mersenne number of the form M M p = 2 2 p − 1 − 1 {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p is prime...

triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...

A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns...

A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the...

composite number is a positive integer that has more divisors than all smaller positive integers. A related concept is that of a largely composite number, a...

In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy...

polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate numbers. The number 10...

Hence χ(0) = 0, χ(1) = χ(2) = χ(4) = 1, and χ(3) = χ(5) = χ(6) = −1. The Jacobsthal matrix Q for GF(q) is the q × q matrix with rows and columns indexed by...

A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...

In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The...

In number theory, a pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1, either from...

In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2...

In number theory, a Carmichael number is a composite number ⁠ n {\displaystyle n} ⁠ which in modular arithmetic satisfies the congruence relation: b n...

numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47...