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

1,2

Links

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

Example

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

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 *)

Crossrefs

Cf. A185300.

Sequence in context: A339093 A072554 A138582 * A362264 A308105 A066309

Adjacent sequences: A215056 A215057 A215058 * A215060 A215061 A215062

Keyword

nonn,base,easy

Author

Michel Lagneau, Aug 01 2012

Status

approved