A225806 Prime(n) such that 2*n^2 - prime(n) is square.

2, 7, 17, 71, 6607, 15313, 91801, 141689, 443777, 858463, 1353593, 2345479, 726919199, 2458927937, 7425764663, 37193744801, 329683117297, 973676004031, 1294734832753, 3825780992497, 10360880429177

Offset

1,1

Comments

The associated indices n are 1, 4, 7, 20, 854, 1789, 8869, 13157, 37247, 68234, ....

a(13) > 6*10^6. - W. Edwin Clark, Jul 25 2013

a(14) > 1.7 * 10^9. - Robert Israel, Apr 13 2020

Links

Table of n, a(n) for n=1..21.

Example

17 is in the sequence because 17 = prime(7) and 2*7^2 - 17 = 81 is square.

Maple

p:=1: count:= 0: R:= NULL: S:= NULL:
for i from 1 while count < 13 do
  p:= nextprime(p);
  if issqr(2*i^2-p) then
    count:= count+1;
    R:= R, p;
    S:= S, i;
  fi
od:
R; # Robert Israel, Apr 13 2020

Prog

(PARI) isok(p) = isprime(p) && issquare(2*primepi(p)^2 - p); \\ Michel Marcus, Apr 14 2020

Crossrefs

Sequence in context: A067602 A216389 A154298 * A283754 A122382 A025554

Adjacent sequences: A225803 A225804 A225805 * A225807 A225808 A225809

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 29 2013

Extensions

a(5)-a(11) from Harvey P. Dale, Jul 22 2013

a(12) from W. Edwin Clark, Jul 25 2013

a(13) from Robert Israel, Apr 13 2020

a(9) corrected and a(14)-a(21) added by Giovanni Resta, Apr 13 2020

Status

approved