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

1,2

Links

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

Example

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

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:

Prog

(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
(Magma) dd:=func<n | [d^2: d in Intseq(n)]>; [n: n in [1..520] | IsPrime(&+dd(n)+&*dd(n))]; // Bruno Berselli, Aug 02 2012

Crossrefs

Cf. A185300.

Sequence in context: A215778 A211021 A364003 * A341162 A205693 A068569

Adjacent sequences: A214743 A214744 A214745 * A214747 A214748 A214749

Keyword

nonn,base,easy

Author

Michel Lagneau, Aug 01 2012

Status

approved