cp's OEIS Frontend

A199169 Primes such that the sum of the squares of their digits equals the number of their digits.

%I A199169 #26 Jan 10 2025 08:39:18
%S A199169 11,102001,1000121,1000211,1002101,1010201,1020011,1020101,1021001,
%T A199169 1102001,1120001,1201001,2001101,2100011,2110001,100012111,100101121,
%U A199169 100110121,100112101,100121011,100211101,101020111,101100211,101102101,101110201,101210101,102100111
%N A199169 Primes such that the sum of the squares of their digits equals the number of their digits.
%C A199169 A subsequence of 1, 11, 111, 1111, 2000, 10002, 10020, 10200, 11111,... which contains n such that A003132(n) = A055642(n). - _R. J. Mathar_, Nov 07 2011
%H A199169 Robert Israel, <a href="/A199169/b199169.txt">Table of n, a(n) for n = 1..10000</a>
%e A199169 a(2) = 102001 is in the sequence because 1^2+0^2+2^2+0^2+0^2+1^2 = 6 = length(a(2)).
%p A199169 g:= proc(n,s) option remember; # <= n-digit numbers with sum of squares of digits = s
%p A199169      option remember; local j;
%p A199169     if s = 0 then return [0]
%p A199169     elif n = 0 then return []
%p A199169     fi;
%p A199169     [seq(op(map(t -> 10*t + j, procname(n-1, s-j^2))),j=0 .. min(9,floor(sqrt(s))))]
%p A199169 end proc:
%p A199169 sort([seq(op(select(t -> t >= 10^(n-1) and isprime(t), g(n,n))),n=1..9)]); # _Robert Israel_, Jan 09 2025
%t A199169 fQ[n_] := Plus @@ (IntegerDigits[n]^2) == IntegerLength[n]; Select[Prime[Range[100000000]], fQ] (* _Robert G. Wilson v_, Nov 07 2011 *)
%Y A199169 Cf. A069710.
%Y A199169 Cf. A003132, A055642.
%K A199169 nonn,base,look
%O A199169 1,1
%A A199169 _Michel Lagneau_, Nov 03 2011