A064545 Lesser of two consecutive primes such that n*p + q is a perfect square, p < q.

17, 7, 2, 23, 23, 17, 449, 13, 773, 7, 2, 1201, 41, 19, 66821, 13, 8191, 2477, 7, 66191, 113, 19, 2, 331, 8209, 27583, 89, 47, 433, 17, 1534751, 37, 2081, 113, 7, 7057, 263, 43, 2, 37, 41737, 4441, 13, 318023, 17, 43, 43801, 71, 23, 7, 11941, 23, 4231, 293

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..62

Example

a(1)=17 because 1*17 + 19 = 36, a square. a(2)=7 because 2*7 + 11 = 25 a square.

Mathematica

Do[k = 1; While[ !IntegerQ[ Sqrt[ n*Prime[k] + Prime[k + 1]]], k++ ]; Print[ Prime[k]], {n, 1, 100} ]

Prog

(PARI) ps(n, k) = k*prime(n)+prime(n+1) k=1; for(n=1, 10^6, if(issquare(ps(n, k)), print1(prime(n), " "); k++; n=0))
(PARI) ps(m, n)= { n*prime(m) + prime(m + 1) } { n=0; default(primelimit, 4294965247); for (n=1, 100, m=1; while (!issquare(ps(m, n)), m++); write("b064545.txt", n, " ", prime(m)) ) } \\ Harry J. Smith, Sep 18 2009

Crossrefs

Cf. A064543.

Sequence in context: A040276 A166211 A086763 * A114032 A107807 A075710

Adjacent sequences: A064542 A064543 A064544 * A064546 A064547 A064548

Keyword

nonn

Author

Jason Earls, Oct 08 2001

Extensions

More terms from Robert G. Wilson v, Oct 09 2001

Status

approved