cp's OEIS Frontend

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

%I A185300 #29 Jul 04 2025 09:13:30
%S A185300 1,11,12,13,15,16,18,19,20,21,23,25,27,29,30,31,32,34,35,37,43,45,50,
%T A185300 51,52,53,54,56,57,58,59,61,65,70,72,73,75,78,79,81,85,87,89,91,92,95,
%U A185300 97,98,101,102,104,106,110,120,140,160,200,201,203,205,209,210,223,225,230,232
%N A185300 Numbers k such that (sum of the decimal digits of k) + (product of the decimal digits of k) is prime.
%H A185300 Robert Israel, <a href="/A185300/b185300.txt">Table of n, a(n) for n = 1..10000</a>
%e A185300 236 is in the sequence because 2 + 3 + 6 + 2*3*6 = 11 + 36 = 47 is prime.
%p A185300 A007953 := proc(n) add(d,d=convert(n,base,10)) ; end proc:
%p A185300 A007954 := proc(n) mul(d,d=convert(n,base,10)) ; end proc:
%p A185300 isA185300 := proc(n) isprime(A007953(n)+A007954(n)) ; end proc:
%p A185300 for n from 1 to 300 do if isA185300(n) then printf("%a,",n) ; end if; end do: # _R. J. Mathar_, Feb 08 2011
%t A185300 Select[Range[235],PrimeQ[DigitSum[#]+Times@@IntegerDigits[#]] &]  (* _Stefano Spezia_, Jun 30 2025 *)
%o A185300 (Magma) [n: n in [1..232] | IsPrime(&+Intseq(n)+&*Intseq(n))]; // _Bruno Berselli_, Aug 02 2012
%o A185300 (PARI) is(n)=my(d=digits(n)); isprime(vecsum(d)+vecprod(d)) \\ _Charles R Greathouse IV_, Jun 06 2017
%Y A185300 Cf. A007953, A007954.
%K A185300 nonn,base,easy
%O A185300 1,2
%A A185300 _Michel Lagneau_, Feb 03 2011