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A103969 Positions n such that A005941(n) = A005940(n). 22

%I

%S 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,

%T 112,128,144,160,192,224,256,288,320,384,448,512,576,640,768,896,1024,

%U 1152,1280,1536,1792,2048,2304,2560,3072,3584,4096,4608,5120,6144,7168

%N Positions n such that A005941(n) = A005940(n).

%C 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

%H R. J. Mathar, <a href="/A103969/b103969.txt">Table of n, a(n) for n = 1..60</a>.

%F Empirical g.f.: x*(1 +x +x^2 +x^3 +x^4)^2 / (1-2*x^5). - _Colin Barker_, Nov 18 2016

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

%t 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]]

%Y Cf. A005940, A005941.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Feb 22 2005

%E Definition corrected and example updated by _R. J. Mathar_, Mar 06 2010

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Last modified May 17 16:03 EDT 2021. Contains 343980 sequences. (Running on oeis4.)