A214746 Numbers n such that (sum of the square of the decimal digits of n) + (product of the square of decimal digits of n) is prime.

1, 11, 13, 16, 19, 29, 31, 37, 59, 61, 73, 79, 91, 92, 95, 97, 101, 102, 104, 106, 110, 120, 140, 160, 201, 203, 205, 207, 210, 225, 230, 238, 250, 252, 270, 283, 302, 308, 320, 328, 380, 382, 401, 405, 409, 410, 449, 450, 490, 494, 502, 504, 506, 508, 520

Offset: 1

Author

Michel Lagneau, Aug 01 2012

Keywords

• nonn
• base
• easy

Examples

			283 is in the sequence because 2^2+8^2+3^2 + 2^2*8^2*3^2 = 77 + 2304 = 2381 is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A185300.

Programs

Magma

dd:=func; [n: n in [1..520] | IsPrime(&+dd(n)+&*dd(n))]; // Bruno Berselli, Aug 02 2012

Maple

A:= proc(n) add(d^2, d=convert(n, base, 10)) ; end proc:
B:= proc(n) mul(d^2, d=convert(n, base, 10)) ; end proc:
isA:= proc(n) isprime(A(n)+B(n)) ; end proc:
for n from 1 to 1000 do if isA(n) then printf("%a, ", n) ; end if; end do:

PARI

is(n)=my(v=eval(Vec(Str(n))));isprime(sum(i=1,#v,v[i]^2)+prod(i=1,#v,v[i]^2)) \\ Charles R Greathouse IV, Aug 02 2012