A185300 Numbers k such that (sum of the decimal digits of k) + (product of the decimal digits of k) is prime.

1, 11, 12, 13, 15, 16, 18, 19, 20, 21, 23, 25, 27, 29, 30, 31, 32, 34, 35, 37, 43, 45, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 65, 70, 72, 73, 75, 78, 79, 81, 85, 87, 89, 91, 92, 95, 97, 98, 101, 102, 104, 106, 110, 120, 140, 160, 200, 201, 203, 205, 209, 210, 223, 225, 230, 232

Offset: 1

Author

Michel Lagneau, Feb 03 2011

Keywords

• nonn
• base
• easy

Examples

			236 is in the sequence because 2 + 3 + 6 + 2*3*6 = 11 + 36 = 47 is prime.
		

Links

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

Crossrefs

Cf. A007953, A007954.

Programs

Magma

[n: n in [1..232] | IsPrime(&+Intseq(n)+&*Intseq(n))]; // Bruno Berselli, Aug 02 2012

Maple

A007953 := proc(n) add(d,d=convert(n,base,10)) ; end proc:
A007954 := proc(n) mul(d,d=convert(n,base,10)) ; end proc:
isA185300 := proc(n) isprime(A007953(n)+A007954(n)) ; end proc:
for n from 1 to 300 do if isA185300(n) then printf("%a,",n) ; end if; end do: # R. J. Mathar, Feb 08 2011

Mathematica

Select[Range[235],PrimeQ[DigitSum[#]+Times@@IntegerDigits[#]] &]  (* Stefano Spezia, Jun 30 2025 *)

PARI

is(n)=my(d=digits(n)); isprime(vecsum(d)+vecprod(d)) \\ Charles R Greathouse IV, Jun 06 2017