

A196815


Smallest index k such that prime(k+n)  prime(k) is a perfect square.


3



1, 2, 14, 1, 4, 2, 18, 9, 7, 3, 29, 21, 19, 12, 8, 4, 2, 31, 21, 19, 11, 1, 59, 4, 2, 22, 24, 15, 16, 8, 6, 3, 36, 37, 174, 21, 18, 11, 12, 63, 78, 189, 38, 2, 27, 25, 112, 1, 107, 12, 6, 4, 45, 169, 28, 33, 21, 112, 14, 9, 10, 6, 4, 44, 37, 153, 151, 29, 27
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OFFSET

1,2


COMMENTS

The corresponding primes are in A196874.


LINKS



EXAMPLE

a(1) = 1 because prime(1) = 2 is the initial prime of a subset of 2 consecutive primes {2, 3} such that 3  2 = 1 = 1^2;
a(3) = 14 because prime(14) = 43 is the initial prime of a subset of 4 consecutive primes {43, 47, 53, 59} such that 59  43 = 16 = 4^2.


MAPLE

for k from 1 do
if issqr(ithprime(k+n)ithprime(k)) then
return k;
end if;
end do:
end proc:


MATHEMATICA

spk[n_]:=Module[{k=1}, While[!IntegerQ[Sqrt[Prime[n+k]Prime[k]]], k++]; k]; Array[spk, 70] (* Harvey P. Dale, Jul 23 2012 *)


PROG

(PARI) a(n) = {my(k=1); while (! issquare(prime(k+n) prime(k)), k++); k; } \\ Michel Marcus, Dec 28 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



