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

1,2

Links

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

Example

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.

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] &]

Prog

(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); }

Crossrefs

Cf. A034968.

Subsequence of A118363, A328205 and A377385.

Subsequences: A377456, A377457.

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

Sequence in context: A014488 A229379 A229371 * A184038 A025407 A025405

Adjacent sequences: A377452 A377453 A377454 * A377456 A377457 A377460

Keyword

nonn,base

Author

Amiram Eldar, Oct 29 2024

Status

approved