A331346 Primes using all the square digits {0, 1, 4, 9} and no others.

1049, 1409, 4019, 4091, 9041, 10499, 10949, 14009, 49019, 49109, 90149, 90401, 94109, 99041, 99401, 100049, 101149, 101419, 101449, 104009, 104119, 104149, 104491, 104911, 104999, 109049, 109141, 109441, 110419, 110491, 111049, 111409, 114901, 140009, 140191, 140419

Offset: 1

Author

K. D. Bajpai, Jan 14 2020

Keywords

• nonn
• base

Comments

Subsequence of A061246.

Examples

			a(1) = 1049 is prime containing all the square digits (0, 1, 4, 9) and no others.
a(2) = 1409 is prime containing all the square digits (0, 1, 4, 9) and no others.
		

Links

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

Crossrefs

Cf. A000040, A061246, A066591, A323387.

Programs

Magma

[p:p in PrimesUpTo(150000)|Set(Intseq(p)) eq {0,1,4,9}]; // Marius A. Burtea, Jan 14 2020

Maple

f:= proc(n) local L,x;
  L:= convert(n,base,4);
  if convert(L,set) <> {0,1,2,3} then return NULL fi;
  L:= subs(2=4,3=9,L);
  x:= add(L[i]*10^(i-1),i=1..nops(L));
  if isprime(x) then x else NULL fi
end proc:
map(f, [$4^3..4^6]); # Robert Israel, Jan 16 2020

Mathematica

Select[FromDigits /@ Tuples[{0, 1, 4, 9}, 6], PrimeQ[#] && Union[IntegerDigits[#]] == {0, 1, 4, 9} &]