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A117725 Zeroless numbers for which the sum of the digits and the product of the digits are both Fibonacci numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
Subsequence of A028840, A028890 and of A052382.
Sequence in context: A070223 A298120 A298205 * A106637 A246361 A228855
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

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Last modified June 19 09:37 EDT 2024. Contains 373501 sequences. (Running on oeis4.)