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

1,1

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

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]

Prog

(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); }

Crossrefs

Subsequence of A380846.

A381074 is a subsequence.

Cf. A380845.

Sequence in context: A221053 A370972 A370970 * A116326 A031809 A252471

Adjacent sequences: A381070 A381071 A381072 * A381074 A381075 A381076

Keyword

nonn,base,new

Author

Amiram Eldar, Feb 13 2025

Status

approved