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

1,2

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.

Links

Table of n, a(n) for n=1..50.

Example

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

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:

Crossrefs

Cf. A003132, A020449, A055016, A067180.

Sequence in context: A173189 A115595 A342123 * A003621 A348006 A338827

Adjacent sequences: A187550 A187551 A187552 * A187554 A187555 A187556

Keyword

nonn,base

Author

Michel Lagneau, Mar 26 2011

Status

approved