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

Author

Dimitris Valianatos, Jul 14 2016

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A226217.

Programs

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 *)

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