A377272 -id:A377272 - cp's OEIS frontend

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

Amiram Eldar, Oct 22 2024

			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.

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

Cf. A007895, A376793 (binary analog).
Subsequence of A328208, A328209 and A377209.
Subsequences: A377272, A377273.

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] &]

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); }

A377457 Numbers k such that k and k+1 are both terms in A377386.

Original entry on oeis.org

1, 12563307224, 15897851550, 30412355999, 37706988600, 52576459775, 67673545631, 118533901904, 244316235000, 297265003100, 332110595000, 340800265728, 349358409503, 375624917760, 378624889440, 416375389115, 450026519903, 561162864248, 596004199840, 728643460544

Offset: 1

Amiram Eldar, Oct 29 2024

			12563307224 is a term since both 12563307224 and 12563307225 are in A377386: 12563307224/A034968(12563307224) = 369509036, 369509036/A034968(369509036) = 9723922 and 9723922/A034968(9723922) = 373997 are integers, and 12563307225/A034968(12563307225) = 358951635, 358951635/A034968(358951635) = 7976703 and 7976703/A034968(7976703) = 257313 are integers.

Amiram Eldar, Table of n, a(n) for n = 1..39

Cf. A034968.
Subsequence of A118363, A328205, A377385, A377386 and A377455.
Analogous sequences: A376795 (binary), A377272 (Zeckendorf).

fdigsum(n) = {my(k = n, m = 2, r, s = 0); while([k, r] = divrem(k, m); k != 0 || r != 0, s += r; m++); s;}
is1(k) = {my(f = fdigsum(k), f2, m); if(k % f, return(0)); m = k/f; f2 = fdigsum(m); !(m % f2) && !((m/f2) % fdigsum(m/f2));}
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}

cp's OEIS Frontend

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

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