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

1, 2, 3, 4, 5, 12, 89, 1824, 3024, 7024, 15084, 17184, 18935, 22624, 28657, 29424, 31464, 37024, 38835, 40032, 42679, 44975, 47375, 66744, 66815, 78219, 89495, 107456, 112175, 119744, 144599, 148519, 169883, 171941, 172025, 188208, 207935, 226624, 244404, 248255

Offset: 1

Author

Amiram Eldar, Oct 22 2024

Keywords

• nonn
• base

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007895, A376793 (binary analog).

Subsequence of A328208, A328209 and A377209.

Subsequences: A377272, A377273.

Programs

Mathematica

zeck[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; (* Alonso del Arte at A007895 *)
q[k_] := q[k] = Module[{z = zeck[k]}, Divisible[k, z] && Divisible[k/z, zeck[k/z]]]; Select[Range[250000], q[#] && q[#+1] &]

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
is1(k) = {my(z = zeck(k)); !(k % z) && !((k/z) % zeck(k/z)); }
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2); }