A279857 - OEIS

%I #25 May 13 2021 11:49:52

%S 5,13,17,29,37,41,53,59,61,71,73,79,83,89,97,101,103,107,109,113,127,

%T 131,137,139,149,151,163,167,179,181,191,197,199,211,223,227,229,233,

%U 239,251,269,271,281

%N Prime numbers p with the property that p is the sum of the squares of two or more distinct one-digit numbers.

%e 5 is in the sequence because 5 = 1^2 + 2^2.

%e 13 is in the sequence because 13 = 2^2 + 3^2.

%t list = {};

%t squares = Subsets[{1,2,3,4,5,6,7,8,9}]^2;

%t For[i=1, i≤Length[squares], i++,

%t     If[PrimeQ[Total[squares[[i]] ]], AppendTo[list, Total[squares[[i]] ]]]];

%t Intersection[list] (* _Robert Price_, Dec 20 2016 *)

%t Select[Union[Total/@Subsets[Range[9]^2,{2,9}]],PrimeQ] (* _Harvey P. Dale_, Jul 20 2020 *)

%o (MiniZinc)

%o % In the modeling language MiniZinc each prime number n belonging to the sequence produces a satisfactory solution for this model:

%o include "all_different.mzn";

%o int: n;

%o var 1..9: A;

%o var 1..9: B;

%o var 1..9: C;

%o var 1..9: D;

%o var 1..9: E;

%o var 1..9: F;

%o var 1..9: G;

%o var 1..9: H;

%o var 1..9: I;

%o var 0..1: nA;var 0..1: nB;var 0..1: nC;var 0..1: nD;var 0..1: nE;var 0..1: nF;var 0..1: nG;var 0..1: nH;var 0..1: nI;

%o solve satisfy;

%o constraint all_different([A,B,C,D,E,F,G,H,I]) /\

%o n=(A*A*nA+B*B*nB+C*C*nC+D*D*nD+E*E*nE+F*F*nF+G*G*nG+H*H*nH+I*I*nI)

%o (Python)

%o from sympy import isprime

%o from itertools import chain, combinations

%o def powerset(s): # skipping empty set and singletons

%o   return chain.from_iterable(combinations(s, r) for r in range(2, len(s)+1))

%o def aupto(limit):

%o   sosds = set(sum(ss) for ss in powerset([i**2 for i in range(1, 10)]))

%o   return sorted(filter(isprime, (t for t in sosds if t <= limit)))

%o print(aupto(281)) # _Michael S. Branicky_, May 13 2021

%K nonn,base,fini,full

%O 1,1

%A _Pierandrea Formusa_, Dec 20 2016