A376795 Numbers k such that k and k+1 are both in A376617.

1, 10624, 13824, 1114112, 2625664, 4563999, 6554624, 16843904, 17266688, 17368064, 20003840, 27137024, 32375160, 32679360, 42993664, 44643599, 63732096, 69222464, 69424640, 70083584, 80778752, 84783104, 85458944, 90256383, 92478000, 116469899, 118063231, 121900544

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

10624 is a term since both 10624 and 10625 are in A376617: 10624/A000120(10624) = 2656, 2656/A000120(2656) = 664, and 664/A000120(664) = 166 are integers, and 10625/A000120(10625) = 2125, 2125/A000120(2125) = 425, and 425/A000120(425) = 85 are integers.

Mathematica

q[k_] := q[k] = Module[{w = DigitCount[k, 2, 1], w2, m, n}, IntegerQ[m = k/w] && Divisible[m, w2 = DigitCount[m, 2, 1]] && Divisible[n = m/w2, DigitCount[n, 2, 1]]]; Select[Range[1.2*10^6], q[#] && q[#+1] &]

Prog

(PARI) s(n) = {my(w = hammingweight(n)); if(w == 1, 0, if(n % w, 1, 1 + s(n/w))); }
is1(k) = {my(sk = s(k)); sk == 0 || sk >= 4; }
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2); }

Crossrefs

Subsequence of A330931, A376617 and A376793.

Cf. A000120.

Sequence in context: A184092 A110018 A249229 * A105304 A009421 A013817

Adjacent sequences: A376792 A376793 A376794 * A376796 A376797 A376798

Keyword

nonn,base

Author

Amiram Eldar, Oct 04 2024

Status

approved