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A113860
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Start with the binary representation of the Catalan constant (A104338, A006752) = 0.91596559... = sum_{i=1..infinity} b(i)/2^i, where b(i)=1,1,1,0,1,0,1,0,0,1,1,1,1.... Then a(n-1)=sum_{i=1..k: sum_{ j = 1..k} b(j)=n} b(i) * 2^(i-1). In words: scan the binary digits of the number, halt at each nonzero binary digit, add a power of 2 corresponding to the place of this digit after the comma, assign current partial sum to a(n), increment n.
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%I #12 Jan 03 2024 07:17:35
%S 1,3,7,23,87,599,1623,3671,7767,15959,81495,343639,867927,1916503,
%T 18693719,152911447,421346903,958217815,2031959639,4179443287,
%U 12769377879,1112281005655,9908374027863,27500560072279,97869304249943
%N Start with the binary representation of the Catalan constant (A104338, A006752) = 0.91596559... = sum_{i=1..infinity} b(i)/2^i, where b(i)=1,1,1,0,1,0,1,0,0,1,1,1,1.... Then a(n-1)=sum_{i=1..k: sum_{ j = 1..k} b(j)=n} b(i) * 2^(i-1). In words: scan the binary digits of the number, halt at each nonzero binary digit, add a power of 2 corresponding to the place of this digit after the comma, assign current partial sum to a(n), increment n.
%C An instance of a Jasinski Integer Sequence using the convention JIS[number,counting system] as defined for example in A080355. This is JIS [Catalan constant,binary]=JIS[0.9159655941772190150546..,2].
%Y Cf. A080355, A080567, A099969, A099970, A099971, A099972.
%K nonn,base
%O 0,2
%A _Artur Jasinski_, Jan 25 2006
%E Naming a sequence after oneself is deprecated. - _N. J. A. Sloane_.
%E Corrected and extended by _R. J. Mathar_, Aug 31 2007
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