A354368 Successive pairs of terms (a, b) such that (a + b) is a square and at least one of a and b is a prime number. This is the lexicographically earliest infinite sequence of distinct terms > 0 with this property.

2, 7, 3, 13, 5, 11, 17, 19, 23, 41, 29, 71, 31, 113, 37, 107, 43, 101, 47, 53, 59, 137, 61, 83, 67, 257, 73, 251, 79, 821, 89, 167, 97, 227, 103, 797, 109, 467, 127, 197, 131, 193, 139, 761, 149, 751, 151, 173, 157, 419, 163, 1601, 179, 397, 181, 719, 191, 293, 199, 701, 211, 1553, 223, 353, 229, 347

Offset

1,1

Comments

This sequence is a permutation of the prime numbers.

Links

Table of n, a(n) for n=1..66.

Michael De Vlieger, Annotated log-log scatterplot of a(n), n = 1..10^4, showing records in red, local minima in blue, and fixed points in gold.

Example

 The earliest pairs with their square sum: (2, 7) = 9, (3, 13) = 16, (5, 11) = 16, (17, 19) = 36, (23, 41) = 64, (29, 71) = 100, (31, 113) = 144, (37, 107) = 144, etc.

Mathematica

nn = 120; c[_] = 0; a[1] = 2; c[2] = 1; u = 3; Do[k = u; If[EvenQ@ i, While[Nand[c[k] == 0, IntegerQ@ Sqrt[# + k]] &[a[i - 1]], k = NextPrime[k]]]; Set[{a[i], c[k]}, {k, i}]; If[k == u, While[c[u] > 0, u = NextPrime[u]]], {i, 2, nn}], i]; Array[a, nn] (* Michael De Vlieger, May 24 2022 *)

Crossrefs

Cf. A354367, A354369, A354370 (same idea).

Sequence in context: A256448 A056756 A120861 * A236542 A279357 A099130

Adjacent sequences: A354365 A354366 A354367 * A354369 A354370 A354371

Keyword

nonn

Author

Eric Angelini and Carole Dubois, May 24 2022

Status

approved