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

11, 102001, 1000121, 1000211, 1002101, 1010201, 1020011, 1020101, 1021001, 1102001, 1120001, 1201001, 2001101, 2100011, 2110001, 100012111, 100101121, 100110121, 100112101, 100121011, 100211101, 101020111, 101100211, 101102101, 101110201, 101210101, 102100111

Offset

1,1

Comments

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

Links

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

Example

a(2) = 102001 is in the sequence because 1^2+0^2+2^2+0^2+0^2+1^2 = 6 = length(a(2)).

Maple

g:= proc(n, s) option remember; # <= n-digit numbers with sum of squares of digits = s
     option remember; local j;
    if s = 0 then return [0]
    elif n = 0 then return []
    fi;
    [seq(op(map(t -> 10*t + j, procname(n-1, s-j^2))), j=0 .. min(9, floor(sqrt(s))))]
end proc:
sort([seq(op(select(t -> t >= 10^(n-1) and isprime(t), g(n, n))), n=1..9)]); # Robert Israel, Jan 09 2025

Mathematica

fQ[n_] := Plus @@ (IntegerDigits[n]^2) == IntegerLength[n]; Select[Prime[Range[100000000]], fQ] (* Robert G. Wilson v, Nov 07 2011 *)

Crossrefs

Cf. A069710.

Cf. A003132, A055642.

Sequence in context: A165934 A110780 A087395 * A145571 A049193 A216596

Adjacent sequences: A199166 A199167 A199168 * A199170 A199171 A199172

Keyword

nonn,base,look,changed

Author

Michel Lagneau, Nov 03 2011

Status

approved