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A103969 Positions n such that A005941(n) = A005940(n). 22
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 24, 28, 32, 36, 40, 48, 56, 64, 72, 80, 96, 112, 128, 144, 160, 192, 224, 256, 288, 320, 384, 448, 512, 576, 640, 768, 896, 1024, 1152, 1280, 1536, 1792, 2048, 2304, 2560, 3072, 3584, 4096, 4608, 5120, 6144, 7168 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence with n>=5 appears to be quintisected with the quintisections multiples of A000079 (powers of two): a(5m) = 5,10,20,40... = 5*2^(m-1) for m>0; a(5m+1) = 6,12,24,48,... = 6*2^(m-1); likewise a(5m+2) = 7*2^(m-1); a(5m+3) = 8*2^(m-1); a(5m+4) = 9*2^(m-1). - Ralf Stephan, Nov 13 2010

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..60.

FORMULA

Empirical g.f.: x*(1 +x +x^2 +x^3 +x^4)^2 / (1-2*x^5). - Colin Barker, Nov 18 2016

EXAMPLE

56 is in the sequence since A005940(56) = A005941(56) = 72.

MATHEMATICA

f[n_] := Block[{p = Partition[ Split[ Join[ IntegerDigits[n - 1, 2], {2}]], 2]}, Times @@ Flatten[ Table[q = Take[p, -i]; Prime[ Count[ Flatten[q], 0] + 1]^q[[1, 1]], {i, Length[p]}] ]]; t = Table[ f[n], {n, 10^4}]; u = Flatten[ Table[ Position[t, n, 1, 1], {n, 10^4}]]; Do[ If[ u[[n]] == {}, u[[n]] = {0}], {n, 10^4}]; Flatten[ Position[ Take[t, 10^4] - Flatten[u], 0]]

CROSSREFS

Cf. A005940, A005941.

Sequence in context: A060472 A130514 A130232 * A271168 A030141 A242367

Adjacent sequences:  A103966 A103967 A103968 * A103970 A103971 A103972

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Feb 22 2005

EXTENSIONS

Definition corrected and example updated by R. J. Mathar, Mar 06 2010

STATUS

approved

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Last modified September 26 01:25 EDT 2017. Contains 292500 sequences.