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

Author

Amiram Eldar, Oct 04 2024

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A330931, A376617 and A376793.

Cf. A000120.

Programs

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] &]

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);}