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A377271 Numbers k such that k and k+1 are both terms in A377209.

%I A377271 #8 Oct 23 2024 00:48:34
%S A377271 1,2,3,4,5,12,89,1824,3024,7024,15084,17184,18935,22624,28657,29424,
%T A377271 31464,37024,38835,40032,42679,44975,47375,66744,66815,78219,89495,
%U A377271 107456,112175,119744,144599,148519,169883,171941,172025,188208,207935,226624,244404,248255
%N A377271 Numbers k such that k and k+1 are both terms in A377209.
%H A377271 Amiram Eldar, <a href="/A377271/b377271.txt">Table of n, a(n) for n = 1..10000</a>
%e A377271 1824 is a term since both 1824 and 1825 are in A377209: 1824/A007895(1824) = 304 and 304/A007895(304) = 76 are integers, and 1825/A007895(1825) = 365 and 365/A007895(365) = 73 are integers.
%t A377271 zeck[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; (* _Alonso del Arte_ at A007895 *)
%t A377271 q[k_] := q[k] = Module[{z = zeck[k]}, Divisible[k, z] && Divisible[k/z, zeck[k/z]]]; Select[Range[250000], q[#] && q[#+1] &]
%o A377271 (PARI) zeck(n) = if(n<4, n>0, my(k=2, s, t); while(fibonacci(k++)<=n, ); while(k && n, t=fibonacci(k); if(t<=n, n-=t; s++); k--); s); \\ _Charles R Greathouse IV_ at A007895
%o A377271 is1(k) = {my(z = zeck(k)); !(k % z) && !((k/z) % zeck(k/z)); }
%o A377271 lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2); }
%Y A377271 Cf. A007895, A376793 (binary analog).
%Y A377271 Subsequence of A328208, A328209 and A377209.
%Y A377271 Subsequences: A377272, A377273.
%K A377271 nonn,base
%O A377271 1,2
%A A377271 _Amiram Eldar_, Oct 22 2024