A215059 Numbers n such that (sum of factorial of decimal digits of n) + (product of factorial of decimal digits of n) is prime.

1, 10, 11, 12, 13, 15, 20, 21, 30, 31, 50, 51, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1200, 1201, 1210, 1211, 1339, 1344, 1345, 1354, 1356, 1359, 1365, 1366, 1368, 1386, 1393, 1395, 1434, 1435, 1443

Offset: 1

Author

Michel Lagneau, Aug 01 2012

Keywords

• nonn
• base
• easy

Examples

			1345 is in the sequence because (1! + 3! + 4! + 5! ) + (1! * 3! * 4! * 5!)  = 151 + 17280 = 17431 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A185300.

Programs

Maple

A:= proc(n) add(d!, d=convert(n, base, 10)) ; end proc:
B:= proc(n) mul(d!, d=convert(n, base, 10)) ; end proc:
isA:= proc(n) isprime(A(n)+B(n)) ; end proc:
for n from 1 to 1500 do if isA(n) then printf("%a, ", n) ; end if; end do:

Mathematica

fdpQ[n_]:=Module[{f=IntegerDigits[n]!},PrimeQ[Total[f]+Times@@f]]; Select[ Range[1500],fdpQ] (* Harvey P. Dale, Nov 26 2013 *)