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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.
0
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Sep 19 2020
STATUS
approved