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%I #34 Jan 04 2024 09:41:37
%S 1,2,3,5,8,11,12,21,111,113,131,311,1112,1115,1121,1124,1142,1151,
%T 1211,1214,1241,1412,1421,1511,2111,2114,2141,2411,4112,4121,4211,
%U 5111,11111,11137,11173,11222,11289,11298,11317,11371,11713,11731,11829,11892,11928
%N Zeroless numbers for which the sum of the digits and the product of the digits are both Fibonacci numbers.
%H Alois P. Heinz, <a href="/A117725/b117725.txt">Table of n, a(n) for n = 1..10000</a>
%H David A. Corneth, <a href="/A117725/a117725.gp.txt">PARI program</a>
%e 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.
%t 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 *)
%o (PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || issquare(k-8); \\ A000045
%o isok(k) = my(d=digits(k)); vecmin(d) && isfib(vecsum(d)) && isfib(vecprod(d)); \\ _Michel Marcus_, Jan 03 2024
%o (PARI) \\ See PARI program in links
%Y Cf. A000045, A117774.
%Y Subsequence of A028840, A028890 and of A052382.
%K base,nonn
%O 1,2
%A Luc Stevens (lms022(AT)yahoo.com), Apr 13 2006
%E a(45) from _J.W.L. (Jan) Eerland_, Jan 03 2024
%E Name clarified by _Michel Marcus_, Jan 03 2024
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