cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A353074 #18 Jan 10 2023 20:32:53
%S A353074 140,148,182,190,242,250,284,292,338,346,410,418,422,430,548,556,578,
%T A353074 586,632,640,692,700,710,718,788,796,812,820,830,838,891,903,920,928,
%U A353074 1022,1030,1040,1048,1052,1060,1154,1162,1172,1180,1250,1258,1336,1352,1400
%N A353074 Numbers that differ from their prime neighbors by distinct squares.
%H A353074 Alois P. Heinz, <a href="/A353074/b353074.txt">Table of n, a(n) for n = 1..10000</a>
%e A353074 Prime neighbors of 891 are 887 and 907, with different square differences 4 and 16. Thus, 891 is in this sequence.
%p A353074 q:= n-> (s-> nops(s)=2 and andmap(issqr, s))({n-prevprime(n), nextprime(n)-n}):
%p A353074 select(q, [$3..2000])[];  # _Alois P. Heinz_, Apr 22 2022
%t A353074 Select[Range[3, 2000], IntegerQ[Sqrt[NextPrime[#] - #]] && IntegerQ[Sqrt[# - Prime[PrimePi[NextPrime[# - 1]] - 1]]] && NextPrime[#] - # != # - Prime[PrimePi[NextPrime[# - 1]] - 1] &]
%o A353074 (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
%Y A353074 Cf. A353072, A353073.
%K A353074 nonn
%O A353074 1,1
%A A353074 _Tanya Khovanova_, Apr 21 2022