login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Primes p for which floor(p/10) is a perfect square.
1

%I #25 Oct 06 2021 12:35:40

%S 11,13,17,19,41,43,47,97,163,167,251,257,367,491,499,641,643,647,811,

%T 1009,1213,1217,1447,1693,1697,1699,2251,2897,3613,3617,4001,4003,

%U 4007,5297,6257,6761,6763,7297,7841,8419,9001,9007,9613,9619

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

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

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

%H Charles R Greathouse IV, <a href="/A275058/b275058.txt">Table of n, a(n) for n = 1..10000</a>

%e For n=9, a(n)=163 is a term because 16 left 3 is square 4^2=16.

%e For n=14, a(n)=491 is a term because 49 left 1 is square 7^2=49.

%t Select[Prime@ Range[5, PrimePi[10^4]], IntegerQ@ Sqrt@ Floor[#/10] &] (* or *)

%t Select[Union@ Flatten@ Map[10 Range[31]^2 + # &, {1, 3, 7, 9}], PrimeQ] (* _Michael De Vlieger_, Jul 14 2016 *)

%o (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

%Y Cf. A226217.

%K nonn,base

%O 1,1

%A _Dimitris Valianatos_, Jul 14 2016