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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A108662.

Sequence in context: A314716 A314717 A314718 * A301291 A314719 A314720

Adjacent sequences: A177146 A177147 A177148 * A177150 A177151 A177152

Keyword

nonn,base

Author

Michel Lagneau, May 03 2010

Status

approved