A274851 Smallest prime q larger than p=prime(n) such that (p+1)(q+1) is a square m^2; a(n)=0 if there is no such q.

11, 0, 23, 17, 47, 223, 31, 79, 53, 269, 71, 151, 167, 1583, 107, 149, 239, 557, 271, 97, 2663, 179, 2099, 359, 127, 2549, 233, 191, 439, 1823, 199, 1187, 2207, 1259, 293, 607, 631, 4099, 1049, 4349, 499, 727, 431, 6983, 3167, 241, 1907, 349, 911, 919, 1663, 1499, 337, 2267, 1031, 593, 479

Offset

1,1

Links

Table of n, a(n) for n=1..57.

Zak Seidov, Table of n, p=prime(n), q=a(n), m=sqrt((p+1)(q+1)), for n=1..102.

Example

n=1: p=2, q=11, (p+1)(q+1)=36=6^2, m=6;
a(2)=0 because there is no q > 3 such that (3+1)(q+1) is a square (because, for prime q >3, (q+1) cannot be a square);
n=3: p = 5, q = 23, (p + 1) (q + 1) = 144 = 12^2, m=12.

Mathematica

Table[SelectFirst[Prime@ Range[n + 1, 10^4], IntegerQ@ Sqrt[(Prime@ n + 1) (# + 1)] &], {n, 102}] /. k_ /; MissingQ@ k -> 0 (* Michael De Vlieger, Jul 09 2016, Version 10.2 *)

Crossrefs

Cf. A274848.

Sequence in context: A297873 A298136 A334370 * A075360 A256756 A087558

Adjacent sequences: A274848 A274849 A274850 * A274852 A274853 A274854

Keyword

nonn

Author

Zak Seidov, Jul 09 2016

Status

approved