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%I #4 Jun 16 2016 23:27:35
%S 1,2,3,7,8,21,61,62,183,547,548,1641,4921,4922,14763,44287,44288,
%T 132861,398581,398582,1195743,3587227,3587228,10761681,32285041,
%U 32285042,96855123,290565367,290565368,871696101,2615088301,2615088302
%N Numbers occurring in A137822 : first differences of numbers n such that 3 | sum( Catalan(k), k=1..2n).
%C This sequence consists of A122983 (which are record values of A137822, i.e. record gaps of A137821), plus the successor of every other term thereof (i.e. A122983(2k+1)+1). See A137822 for more details & formulas.
%C The (very simple) sequence A137824 gives the index of A137822 at which A137823(n) occurs for the first time.
%o (PARI) A137823(n) = (n%3==2)+3^((n-1)*2\3+1)\4+1
%Y Cf. A107755, A122983, A137821-A137824.
%K nonn,easy
%O 1,2
%A _M. F. Hasler_, May 15 2008
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