A117725 Zeroless numbers for which the sum of the digits and the product of the digits are both Fibonacci numbers.

1, 2, 3, 5, 8, 11, 12, 21, 111, 113, 131, 311, 1112, 1115, 1121, 1124, 1142, 1151, 1211, 1214, 1241, 1412, 1421, 1511, 2111, 2114, 2141, 2411, 4112, 4121, 4211, 5111, 11111, 11137, 11173, 11222, 11289, 11298, 11317, 11371, 11713, 11731, 11829, 11892, 11928

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 13 2006

Keywords

• base
• nonn

Examples

			18192 is a term because the sum of its digits is 1+8+1+9+2 = 21, the product of its digits is 1*8*1*9*2 = 144 and both 21 and 144 are Fibonacci numbers.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• David A. Corneth, PARI program

Crossrefs

Cf. A000045, A117774.

Subsequence of A028840, A028890 and of A052382.

Programs

Mathematica

isFibonacci[x_]:=MemberQ[Array[Fibonacci,2x],x];DeleteCases[ParallelTable[If[And[isFibonacci[Times@@IntegerDigits[n]],isFibonacci[Total[IntegerDigits[n]]]],n,a],{n,1,15000}],a] (* J.W.L. (Jan) Eerland, Jan 03 2024 *)

PARI

isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || issquare(k-8); \\ A000045
isok(k) = my(d=digits(k)); vecmin(d) && isfib(vecsum(d)) && isfib(vecprod(d)); \\ Michel Marcus, Jan 03 2024

PARI

\\ See PARI program in links

Extensions

a(45) from J.W.L. (Jan) Eerland, Jan 03 2024

Name clarified by Michel Marcus, Jan 03 2024