

A353072


Numbers k such that nextprime(k)k is a positive square.


3



1, 2, 4, 6, 7, 10, 12, 13, 16, 18, 19, 22, 25, 28, 30, 33, 36, 37, 40, 42, 43, 46, 49, 52, 55, 58, 60, 63, 66, 67, 70, 72, 75, 78, 79, 82, 85, 88, 93, 96, 97, 100, 102, 103, 106, 108, 109, 112, 118, 123, 126, 127, 130, 133, 136, 138, 140, 145, 148, 150, 153
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OFFSET

1,2


COMMENTS

Numbers p1, where p is prime is a subsequence (see A006093).


LINKS



EXAMPLE

The next prime after 7 is 11, and 117 = 4 a square, so 7 is in this sequence.
The next prime after 118 is 127, 127118 = 9 is a square, so 118 is a term.


MATHEMATICA

Select[Range[2000], NextPrime[#]  # > 0 && IntegerQ[Sqrt[NextPrime[#]  #]] &]
npsQ[n_]:=With[{c=NextPrime[n]n}, c>0&&IntegerQ[Sqrt[c]]]; Select[Range[200], npsQ] (* Harvey P. Dale, May 05 2023 *)


PROG

(PARI) upto(n) = {my(res = List(1), q = 2, u = nextprime(n + 1)); forprime(p = 3, u, forstep(i = sqrtint(p  q), 1, 1, listput(res, pi^2) ); q = p ); res } \\ David A. Corneth, Apr 22 2022
(PARI) isok(k) = issquare(nextprime(k+1)k); \\ Michel Marcus, Apr 22 2022


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



