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A381074 Numbers k such that k, k+2 and k+4 are all terms in A380846.

%I A381074 #6 Feb 17 2025 03:29:18
%S A381074 10820236,24069388,27802288,39297580,50717488,56362960,73070224,
%T A381074 97339504,103605964,112209580,112526032,140053564,145315600,155790124,
%U A381074 156415084,158877232,184667248,185979664,188913004,189225484,189541936,224435536,281740396,292406380,314388112
%N A381074 Numbers k such that k, k+2 and k+4 are all terms in A380846.
%C A381074 Numbers k such that A380845(k) = 2*k, A380845(k+2) = 2*(k+2), and A380845(k+4) = 2*(k+4).
%H A381074 Amiram Eldar, <a href="/A381074/b381074.txt">Table of n, a(n) for n = 1..1000</a>
%t A381074 f[n_] := Module[{h = DigitCount[n, 2, 1]}, DivisorSum[n, # &, DigitCount[#, 2, 1] == h &] == 2*n]; seq[lim_] := Module[{q = Table[False, {6}], s = {}}, q[[1 ;; 4]] = f /@ Range[4]; Do[q[[5 ;; 6]] = f /@ Range[k, k + 1]; If[q[[1]] && q[[3]] && q[[5]], AppendTo[s, k - 4]]; If[q[[2]] && q[[4]] && q[[6]], AppendTo[s, k - 3]]; q[[1 ;; 4]] = q[[3 ;; 6]], {k, 5, lim, 2}]; s]; seq[11000000]
%o A381074 (PARI) is1(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) == 2*k;}
%o A381074 list(lim) = {my(q1 = is1(1), q2 = is1(2), q3 = is1(3), q4 = is1(4), q5, q6); forstep(k = 5, lim, 2, q5 = is1(k); q6 = is1(k+1); if(q1 && q3 && q5, print1(k-4, ", ")); if(q2 && q4 && q6, print1(k-3, ", ")); q1 = q3; q2 = q4; q3 = q5; q4 = q6);}
%Y A381074 Subsequence of A380846 and A381073.
%Y A381074 Cf. A380845.
%K A381074 nonn,base
%O A381074 1,1
%A A381074 _Amiram Eldar_, Feb 13 2025