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A353074
Numbers that differ from their prime neighbors by distinct squares.
1
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
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
Sequence in context: A252963 A114825 A308617 * A224982 A256085 A054573
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Apr 21 2022
STATUS
approved