A377455 Numbers k such that k and k+1 are both terms in A377385.

1, 1224, 126191, 428519, 649727, 1015416, 1988064, 3425856, 4542740, 4574240, 4743900, 4813668, 5131008, 6899840, 7001315, 7172424, 7356096, 8020583, 10206000, 11146421, 11566800, 11597999, 11693807, 12556700, 13742624, 13745759, 13831487, 14365120, 16939799, 20561400

Offset: 1

Author

Amiram Eldar, Oct 29 2024

Keywords

• nonn
• base

Examples

			1224 is a term since both 1224 and 1225 are in A377385: 1224/A034968(1224) = 204 and 204/A034968(204) = 34 are integers, and 1225/A034968(1225) = 175 and 175/A034968(175) = 35 are integers.
		

Links

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

Crossrefs

Cf. A034968.

Subsequence of A118363, A328205 and A377385.

Subsequences: A377456, A377457.

Analogous sequences: A376793 (binary), A377271 (Zeckendorf).

Programs

Mathematica

fdigsum[n_] := Module[{k = n, m = 2, r, s = 0}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, s += r; m++]; s]; q[k_] := q[k] = Module[{f = fdigsum[k]}, Divisible[k, f] && Divisible[k/f, fdigsum[k/f]]]; Select[Range[2*10^6], q[#] && q[#+1] &]

PARI

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