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

1,1

Links

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

Example

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

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] &]

Prog

(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

Crossrefs

Cf. A353072, A353073.

Sequence in context: A252963 A114825 A308617 * A224982 A256085 A054573

Adjacent sequences: A353071 A353072 A353073 * A353075 A353076 A353077

Keyword

nonn

Author

Tanya Khovanova, Apr 21 2022

Status

approved