A377272 Numbers k such that k and k+1 are both terms in A377210.

1, 2, 3, 4, 5, 12, 47375, 2310399, 3525200, 6506367, 9388224, 17613504, 29373839, 41534800, 48191759, 48344120, 66927384, 68094999, 71982999, 92547279, 95497919, 110146959, 110395439, 126123920, 148865535, 152546030, 154451583, 171570069, 193628799, 232058519

Offset: 1

Author

Amiram Eldar, Oct 22 2024

Keywords

• nonn
• base

Examples

			47375 is a term since both 47375 and 47376 are in A377210: 47375/A007895(47375) = 9475, 9475/A007895(9475) = 1895 and 1895/A007895(1895) = 379 are integers, and 47376/A007895(47376) = 15792, 15792/A007895(15792) = 3948 and 3948/A007895(3948) = 1316 are integers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..370

Crossrefs

Cf. A007895, A376795 (binary analog).

Subsequence of A328208, A328209, A377210 and A377271.

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], z2, m, n}, IntegerQ[m = k/z] && Divisible[m, z2 = zeck[m]] && Divisible[n = m/z2, zeck[n]]]; Select[Range[50000], 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), z2, m); if(k % z, return(0)); m = k/z; z2 = zeck(m); !(m % z2) && !((m/z2) % zeck(m/z2)); }
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2); }