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

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

David A. Corneth, PARI program

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000045, A117774.

Subsequence of A028840, A028890 and of A052382.

Sequence in context: A070223 A298120 A298205 * A106637 A246361 A228855

Adjacent sequences: A117722 A117723 A117724 * A117726 A117727 A117728

Keyword

base,nonn

Author

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

Extensions

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

Name clarified by Michel Marcus, Jan 03 2024

Status

approved