A177149 Indices n such that the sums of the squares of the digits of prime(n) are prime.

5, 9, 13, 18, 23, 26, 30, 32, 33, 40, 41, 43, 45, 46, 48, 50, 64, 65, 66, 67, 68, 71, 74, 75, 78, 79, 80, 86, 87, 89, 90, 91, 110, 116, 117, 118, 121, 124, 128, 130, 131, 137, 139, 145, 150, 153, 156, 157, 159, 164, 165, 167, 168, 170, 171, 173, 174, 182, 184, 185

Offset: 1

Author

Michel Lagneau, May 03 2010

Keywords

• nonn
• base

Comments

n such that prime(n) is in A108662. - Robert Israel, Aug 05 2019

Examples

			5 is in the sequence because the 5th prime is 11, and 1^2 + 1^2 = 2 prime;
9 is in the sequence because the 9th prime is 23, and 2^2 + 3^2 = 13 prime;
139 is in the sequence because the 139th prime is 797, and 7^2 + 9^2 + 7^2 =179 prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A108662.

Programs

Maple

with(numtheory): nn:= 150: T:=array(1..nn):k:=1:for n from 1 to 731 do:p:=ithprime(n):l:=evalf(floor(ilog10(p))+1):n0:=p:s:=0:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v :s:=s+u^2:od:if type(s,prime)=true then T[k]:=n:k:=k+1: else fi:od:print(T):
# Simpler:
filter:= proc(n) isprime(add(t^2,t=convert(ithprime(n),base,10))) end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 05 2019

Mathematica

Select[Range[200],PrimeQ[Total[IntegerDigits[Prime[#]]^2]]&] (* Harvey P. Dale, Jan 10 2021 *)