A187553 Smallest prime p such that the sum of the squares of the digits of p equals n (or 0 if no such prime exists).

0, 11, 0, 2, 101111, 211, 2111, 101111111, 3, 13, 113, 112121, 23, 21221, 1123, 11213, 41, 1223, 313, 10133, 241, 233, 112223, 21313, 5, 431, 151, 1151, 13313, 251, 2333, 11251, 2243, 53, 1433, 1153, 61, 523, 1523, 11161, 443, 541, 353, 33413, 2621, 163, 1163, 13523, 7, 17

Offset: 1

Author

Michel Lagneau, Mar 26 2011

Keywords

• nonn
• base

Comments

a(3) = 0 because the numbers of the form 10..010..01 are divisible by 3. Conjecture : except for the numbers 1 and 3, for every possible square digit sum there exists a prime.

Examples

			a(13) = 23 because 2^2 + 3^2 = 13, and 23 is the least such prime.
		

Crossrefs

Cf. A003132, A020449, A055016, A067180.

Programs

Maple

with(numtheory):for k from 2 to 100 do: id:=0:for p from 1 to 100000 while(id=0)
  do:n:=ithprime(p):l:=length(n):n0:=n: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 s=k then id:=1:printf(`%d, `,n):else fi:od:od: