A353074 Numbers that differ from their prime neighbors by distinct squares.

140, 148, 182, 190, 242, 250, 284, 292, 338, 346, 410, 418, 422, 430, 548, 556, 578, 586, 632, 640, 692, 700, 710, 718, 788, 796, 812, 820, 830, 838, 891, 903, 920, 928, 1022, 1030, 1040, 1048, 1052, 1060, 1154, 1162, 1172, 1180, 1250, 1258, 1336, 1352, 1400

Offset: 1

Author

Tanya Khovanova, Apr 21 2022

Keywords

• nonn

Examples

			Prime neighbors of 891 are 887 and 907, with different square differences 4 and 16. Thus, 891 is in this sequence.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A353072, A353073.

Programs

Maple

q:= n-> (s-> nops(s)=2 and andmap(issqr, s))({n-prevprime(n), nextprime(n)-n}):
select(q, [$3..2000])[];  # Alois P. Heinz, Apr 22 2022

Mathematica

Select[Range[3, 2000], IntegerQ[Sqrt[NextPrime[#] - #]] && IntegerQ[Sqrt[# - Prime[PrimePi[NextPrime[# - 1]] - 1]]] && NextPrime[#] - # != # - Prime[PrimePi[NextPrime[# - 1]] - 1] &]

PARI

isok(k) = my(d,dd); (k>1) && issquare(nextprime(k+1)-k, &d) && issquare(k-precprime(k-1), &dd) && (d!=dd); \\ Michel Marcus, Apr 22 2022