A350554 a(1) = 0; for n>0, a(n) is the smallest k in A350552 which is not yet a term and is such that k + a(n-1) is in A350552.

0, 2, 4, 16, 6, 99, 9, 40, 20, 22, 27, 38, 78, 86, 68, 42, 133, 134, 96, 52, 65, 45, 60, 88, 104, 100, 114, 110, 175, 49, 69, 105, 154, 108, 116, 262, 118, 144, 148, 164, 192, 166, 184, 174, 204, 212, 117, 209, 245, 214, 216, 232, 256, 292, 336, 224, 230, 310

Offset

1,2

Links

Table of n, a(n) for n=1..58.

Example

a(2) = 2 = 10_2 and a(2)' = 2' = 1 = 1_2 have a single 1 in their binary expansion, a(1) + a(2) = 0 + 2 = 10_2 and (a(1) + a(2))' = (0 + 2)' = 2' = 1 = 1_2 have a single 1 in their binary expansion.
a(3) = 4 = 100_2, a(3)' = 4' = 4 = 100_2 have a single 1 in their binary expansion, and a(2) + a(3) = 2 + 4 = 6 = 110_2 and (a(2) + a(3))' = (2 + 4)' = 6' = 5 = 101_2, have two 1's in their binary expansion.

Mathematica

d[0] = d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); v = Select[Range[0, 600], Equal @@ DigitCount[{#, d[#]}, 2, 1] &]; s = {}; found = True; i = {1}; While[i != {}, AppendTo[s, v[[i[[1]]]]]; i = FirstPosition[v, _?(! MemberQ[s, #] && MemberQ[v, s[[-1]] + #] &)]]; s (* Amiram Eldar, Jan 27 2022 *)

Prog

(Magma) f:=func<n |n le 1 select 0 else  n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; ham:=func<a, b|Multiplicity(Intseq(a, 2), 1) eq Multiplicity(Intseq(b, 2), 1)>; a:=[0]; for n in [2..57] do k:=1; while k in a or not ham(k, Floor(f(k))) or not ham(k+a[n-1], Floor(f(k+a[n-1]))) do k:=k+1; end while;  Append(~a, k); end for; a;

Crossrefs

Cf. A000120, A003415, A350552.

Sequence in context: A217291 A364247 A338839 * A094670 A110005 A019540

Adjacent sequences: A350551 A350552 A350553 * A350555 A350556 A350557

Keyword

nonn,base

Author

Marius A. Burtea, Jan 24 2022

Status

approved