A376793 - OEIS

%I #9 Oct 05 2024 14:04:53

%S 1,1424,2484,4304,4655,6223,10624,13824,20624,22784,29448,33424,33984,

%T 36944,41535,43263,45184,45324,65744,66199,68624,69632,70784,74304,

%U 74627,99584,103103,103424,105720,114704,120680,139904,147636,164224,166144,192576,199968

%N Numbers k such that k and k+1 are both in A376616.

%H Amiram Eldar, <a href="/A376793/b376793.txt">Table of n, a(n) for n = 1..10000</a>

%e 1424 is a term since both 1424 and 1425 are in A376616: 1424/A000120(1424) = 356 and 356/A000120(356) = 89 are integers, and 1425/A000120(1425) = 285 and 285/A000120(285) = 57 are integers.

%t q[k_] := q[k] = Module[{w = DigitCount[k, 2, 1]}, Divisible[k, w] && Divisible[k/w, DigitCount[k/w, 2, 1]]]; Select[Range[20000], q[#] && q[#+1] &]

%o (PARI) is1(k) = {my(w = hammingweight(k)); !(k % w) && !((k/w) % hammingweight(k/w));}

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

%Y Subsequence of A330931 and A376616.

%Y Subsequences: A376794, A376795.

%Y Cf. A000120.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Oct 04 2024