A337773 Positive even integers that do not have a Goldbach partition (p,q) such that at least one of p+-1 or q+-1 is a positive square.

2, 38, 122, 128, 158, 192, 206, 212, 222, 224, 290, 302, 326, 332, 338, 380, 398, 428, 440, 488, 518, 530, 542, 548, 554, 626, 632, 692, 752, 782, 836, 872, 878, 902, 938, 962, 968, 992, 1082, 1136, 1142, 1172, 1182, 1202, 1214, 1244, 1256, 1298, 1352, 1362, 1382, 1472, 1512

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Eric Weisstein's World of Mathematics, Goldbach Partition

Wikipedia, Goldbach's conjecture

Index entries for sequences related to Goldbach conjecture

Index entries for sequences related to partitions

Example

a(2) = 38 is in the sequence since it has two Goldbach partitions, (31,7) and (13,13) but none of 31+-1, 7+-1, 13+-1 are squares.

Mathematica

Table[If[Sum[Sign[(Floor[Sqrt[i - 1]] - Floor[Sqrt[i - 2]]) + (Floor[Sqrt[2 n - i - 1]] - Floor[Sqrt[2 n - i - 2]]) + (Floor[Sqrt[i + 1]] - Floor[Sqrt[i]]) + (Floor[Sqrt[2 n - i + 1]] - Floor[Sqrt[2 n - i]])]* (PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {i, n}] == 0, 2 n, {}], {n, 300}] // Flatten

Crossrefs

Cf. A010051, A010052, A045917, A337772.

Sequence in context: A294396 A075459 A050248 * A364714 A105645 A098456

Adjacent sequences: A337770 A337771 A337772 * A337774 A337775 A337776

Keyword

nonn

Author

Wesley Ivan Hurt, Sep 19 2020

Status

approved