cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A131511 All possible products of prime and Fibonacci numbers.

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%I A131511 #13 Apr 20 2018 11:46:15
%S A131511 0,2,3,4,5,6,7,9,10,11,13,14,15,16,17,19,21,22,23,24,25,26,29,31,33,
%T A131511 34,35,37,38,39,40,41,42,43,46,47,51,53,55,56,57,58,59,61,62,63,65,67,
%U A131511 68,69,71,73,74,79,82,83,85,86,87,88,89,91,93,94,95,97,101,102,103,104,105
%N A131511 All possible products of prime and Fibonacci numbers.
%C A131511 This sequence contains all prime numbers as a subsequence because 1 is a Fibonacci number. Similarly it contains all even semiprimes.
%H A131511 G. C. Greubel, <a href="/A131511/b131511.txt">Table of n, a(n) for n = 1..5000</a>
%e A131511 8 is not in this sequence because the only way to represent 8 as a product of a prime and some number is 2*4 and 4 is not a Fibonacci number.
%e A131511 105 is in this sequence because 105 = 3*21 and 3 is a prime number and 21 is a Fibonacci number.
%t A131511 Take[Union[Flatten[Table[Fibonacci[n]*Prime[k], {n, 70}, {k, 70}]]], 70]
%o A131511 (PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
%o A131511 isok(n) = {if (n==0, return (1)); my(f=factor(n)); for (k=1, #f~, p = f[k, 1]; if (isfib(n/p), return (1)););} \\ _Michel Marcus_, Apr 19 2018
%Y A131511 Cf. A000045, A001358, A049997, A132147.
%K A131511 nonn
%O A131511 1,2
%A A131511 _Tanya Khovanova_, Aug 14 2007