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 A137824 Index at which A137823(n) occurs first in A137822 (gaps in numbers m such that 3 | sum( Catalan(k), k=1..2m)). 7
 1, 3, 2, 4, 12, 8, 16, 48, 32, 64, 192, 128, 256, 768, 512, 1024, 3072, 2048, 4096, 12288, 8192, 16384, 49152, 32768, 65536, 196608, 131072, 262144, 786432, 524288, 1048576, 3145728, 2097152, 4194304, 12582912, 8388608, 16777216, 50331648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Other characterization of the sequence: concatenate pattern (1,3,2) multiplying it by 4 after each concatenation step. Or: Start with 1,3,2, then iteratively append the whole sequence obtained so far multiplied by 4^(length of the sequence divided by 3) See A137822 and A137823 for more comments and formulas. LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,4). FORMULA If n=2 (mod 3) then a(n) = 3*2^[2(n-1)/3]; else a(n) = 2^[(2(n-1)/3]. a(n) = 4*a(n-3) for n>3. G.f.: x*(1+x)*(1+2*x)/(1-4*x^3). [Colin Barker, Aug 19 2012] PROG (PARI) A137824(n) = if( n%3==2, 3, 1)<<(2*(n-1)\3) (PARI) A137824(n) = for( i=1, #A137822, A137822[i]==A137823[n] & return(i)) (PARI) a=[1, 3, 2]; for( i=1, 5, a=concat( a, 4^(#a/3)*a )); a CROSSREFS Cf. A107755, A122983, A137821-A137823. Sequence in context: A319103 A332647 A290333 * A019321 A336435 A279261 Adjacent sequences:  A137821 A137822 A137823 * A137825 A137826 A137827 KEYWORD nonn,easy AUTHOR M. F. Hasler, May 15 2008 STATUS approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)