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%I #8 Oct 05 2024 14:04:59
%S 38143807,67141710,67511743,67736383,269912383,675612223,1251282942,
%T 2216832254,4135244542,4213075438,4256878846,4608511334,5089851270,
%U 5148094783,5383281343,5457887279,5905845439,7247769919,7355297535,7811735295,8209151742,8503999231,8591105023,9015656767
%N Starts of runs of 3 consecutive integers that are in A376616.
%H Amiram Eldar, <a href="/A376794/b376794.txt">Table of n, a(n) for n = 1..250</a>
%e 38143807 is a term since 38143807, 38143808 and 38143809 are all in A376616: 38143807/A000120(38143807) = 2934139, and 2934139/A000120(2934139) = 225703 are integers, 38143808/A000120(38143808) = 4767976, and 4767976/A000120(4767976) = 595997 are integers, and 38143809/A000120(38143809) = 4238201, and 4238201/A000120(4238201) = 385291 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[10^8], q[#] && q[#+1] && q[#+2] &]
%o (PARI) is1(k) = {my(w = hammingweight(k)); !(k % w) && !((k/w) % hammingweight(k/w));}
%o lista(kmax) = {my(q1 = is1(1), q2 = is1(2), q3); for(k = 3, kmax, q3 = is1(k); if(q1 && q2 && q3, print1(k-2, ", ")); q1 = q2; q2 = q3);}
%Y Subsequence of A330932, A376616 and A376793.
%Y Cf. A000120.
%K nonn,base
%O 1,1
%A _Amiram Eldar_, Oct 04 2024