A279857 Prime numbers p with the property that p is the sum of the squares of two or more distinct one-digit numbers.

5, 13, 17, 29, 37, 41, 53, 59, 61, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 163, 167, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 251, 269, 271, 281

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Example

5 is in the sequence because 5 = 1^2 + 2^2.
13 is in the sequence because 13 = 2^2 + 3^2.

Mathematica

list = {};
squares = Subsets[{1, 2, 3, 4, 5, 6, 7, 8, 9}]^2;
For[i=1, i≤Length[squares], i++,
    If[PrimeQ[Total[squares[[i]] ]], AppendTo[list, Total[squares[[i]] ]]]];
Intersection[list] (* Robert Price, Dec 20 2016 *)
Select[Union[Total/@Subsets[Range[9]^2, {2, 9}]], PrimeQ] (* Harvey P. Dale, Jul 20 2020 *)

Prog

(MiniZinc)
% In the modeling language MiniZinc each prime number n belonging to the sequence produces a satisfactory solution for this model:
include "all_different.mzn";
int: n;
var 1..9: A;
var 1..9: B;
var 1..9: C;
var 1..9: D;
var 1..9: E;
var 1..9: F;
var 1..9: G;
var 1..9: H;
var 1..9: I;
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;
solve satisfy;
constraint all_different([A, B, C, D, E, F, G, H, I]) /\
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)
(Python)
from sympy import isprime
from itertools import chain, combinations
def powerset(s): # skipping empty set and singletons
  return chain.from_iterable(combinations(s, r) for r in range(2, len(s)+1))
def aupto(limit):
  sosds = set(sum(ss) for ss in powerset([i**2 for i in range(1, 10)]))
  return sorted(filter(isprime, (t for t in sosds if t <= limit)))
print(aupto(281)) # Michael S. Branicky, May 13 2021

Crossrefs

Sequence in context: A265889 A359151 A191218 * A077426 A231754 A175768

Adjacent sequences: A279854 A279855 A279856 * A279858 A279859 A279860

Keyword

nonn,base,fini,full

Author

Pierandrea Formusa, Dec 20 2016

Status

approved