A275058 Primes p for which floor(p/10) is a perfect square.

11, 13, 17, 19, 41, 43, 47, 97, 163, 167, 251, 257, 367, 491, 499, 641, 643, 647, 811, 1009, 1213, 1217, 1447, 1693, 1697, 1699, 2251, 2897, 3613, 3617, 4001, 4003, 4007, 5297, 6257, 6761, 6763, 7297, 7841, 8419, 9001, 9007, 9613, 9619

Offset

1,1

Comments

Terms are of the form 10*k^2 + t, with gcd(t, 10) = 1, i.e., {1, 3, 7, 9}.

Sum_{n>=1} 1/a(n) = 0.403068... converges.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

For n=9, a(n)=163 is a term because 16 left 3 is square 4^2=16.
For n=14, a(n)=491 is a term because 49 left 1 is square 7^2=49.

Mathematica

Select[Prime@ Range[5, PrimePi[10^4]], IntegerQ@ Sqrt@ Floor[#/10] &] (* or *)
Select[Union@ Flatten@ Map[10 Range[31]^2 + # &, {1, 3, 7, 9}], PrimeQ] (* Michael De Vlieger, Jul 14 2016 *)

Prog

(PARI) for(n=1, 1e3, forstep(p=10*n^2+1, 10*n^2+9, [2, 4, 2], if(isprime(p), print1(p", ")))) \\ Charles R Greathouse IV, Jul 15 2016

Crossrefs

Cf. A226217.

Sequence in context: A068155 A271367 A226217 * A157175 A132244 A262731

Adjacent sequences: A275055 A275056 A275057 * A275059 A275060 A275061

Keyword

nonn,base

Author

Dimitris Valianatos, Jul 14 2016

Status

approved