A381073 Numbers k such that k and k+2 are both terms in A380846.

8596, 9772, 10444, 17836, 19626, 21196, 23716, 27186, 35754, 36484, 38164, 42700, 45892, 54796, 56586, 85708, 91252, 98586, 100770, 104970, 112698, 132412, 136612, 139074, 140980, 141652, 144676, 149716, 152850, 165172, 166122, 171724, 182032, 182644, 184770, 190482

Offset: 1

Author

Amiram Eldar, Feb 13 2025

Keywords

• nonn
• base

Comments

Numbers k such that A380845(k) = 2*k and A380845(k+2) = 2*(k+2).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A380846.

A381074 is a subsequence.

Cf. A380845.

Programs

Mathematica

f[n_] := Module[{h = DigitCount[n, 2, 1]}, DivisorSum[n, # &, DigitCount[#, 2, 1] == h &] == 2*n]; seq[lim_] := Module[{q = Table[False, {4}], s = {}}, q[[1 ;; 2]] = f /@ Range[2]; Do[q[[3 ;; 4]] = f /@ Range[k, k + 1]; If[q[[1]] && q[[3]], AppendTo[s, k - 2]]; If[q[[2]] && q[[4]], AppendTo[s, k - 1]]; q[[1 ;; 2]] = q[[3 ;; 4]], {k, 3, lim, 2}]; s]; seq[50000]

PARI

is1(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) == 2*k;}
list(lim) = {my(q1 = is1(1), q2 = is1(2), q3, q4); forstep(k = 3, lim, 2, q3 = is1(k); q4 = is1(k+1); if(q1 && q3, print1(k-2, ", ")); if(q2 && q4, print1(k-1, ", ")); q1 = q3; q2 = q4);}