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

1,2

Links

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

Example

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.

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] &]

Prog

(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); }

Crossrefs

Cf. A007895, A376795 (binary analog).

Subsequence of A328208, A328209, A377210 and A377271.

Sequence in context: A165303 A109744 A377271 * A065635 A325693 A367140

Adjacent sequences: A377269 A377270 A377271 * A377273 A377274 A377275

Keyword

nonn,base

Author

Amiram Eldar, Oct 22 2024

Status

approved