A381582 Numbers k such that k and k+1 are both terms in A381581.

1, 2, 3, 20, 21, 27, 44, 55, 56, 57, 75, 95, 110, 111, 115, 152, 175, 207, 264, 287, 291, 304, 305, 344, 364, 365, 377, 380, 395, 398, 399, 404, 425, 435, 455, 534, 584, 605, 815, 846, 847, 864, 888, 930, 987, 992, 1004, 1011, 1024, 1025, 1064, 1084, 1085, 1145, 1182

Offset: 1

Author

Amiram Eldar, Feb 28 2025

Keywords

• nonn
• easy
• base

Comments

If k is not divisible by 3 (A001651), then A001906(k) = Fibonacci(2*k) is a term.

Examples

			1 is a term since A291711(1) = 1 divides 1 and A291711(2) = 2 divides 2.
20 is a term since A291711(20) = 4 divides 20 and A291711(21) = 1 divides 21.
		

Links

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

Crossrefs

Cf. A000045, A001906, A001651, A291711.

Subsequence of A381581.

Subsequences: A381583, A381584, A381585.

Similar sequences: A328209, A330927, A330931, A351720.

Programs

Mathematica

f[n_] := f[n] = Fibonacci[2*n]; q[n_] := q[n] = Module[{s = 0, m = n, k}, While[m > 0, k = 1; While[m > f[k], k++]; If[m < f[k], k--]; If[m >= 2*f[k], s += 2; m -= 2*f[k], s++; m -= f[k]]]; Divisible[n, s]]; Select[Range[1200], q[#] && q[#+1] &]

PARI

mx = 20; fvec = vector(mx, i, fibonacci(2*i)); f(n) = if(n <= mx, fvec[n], fibonacci(2*n));
is1(n) = {my(s = 0, m = n, k); while(m > 0, k = 1; while(m > f(k), k++); if(m < f(k), k--); if(m >= 2*f(k), s += 2; m -= 2*f(k), s++; m -= f(k))); !(n % s);}
list(lim) = {my(q1 = is1(1), q2); for(k = 2, lim, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}