A377272 - OEIS

%I #7 Oct 23 2024 00:48:47

%S 1,2,3,4,5,12,47375,2310399,3525200,6506367,9388224,17613504,29373839,

%T 41534800,48191759,48344120,66927384,68094999,71982999,92547279,

%U 95497919,110146959,110395439,126123920,148865535,152546030,154451583,171570069,193628799,232058519

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

%H Amiram Eldar, <a href="/A377272/b377272.txt">Table of n, a(n) for n = 1..370</a>

%e 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.

%t zeck[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; (* _Alonso del Arte_ at A007895 *)

%t 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] &]

%o (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 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)); }

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

%Y Cf. A007895, A376795 (binary analog).

%Y Subsequence of A328208, A328209, A377210 and A377271.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Oct 22 2024