

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(n1) is in A350552.


0



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
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OFFSET

1,2


LINKS



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, bMultiplicity(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[n1], Floor(f(k+a[n1]))) do k:=k+1; end while; Append(~a, k); end for; a;


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



