A137823 Numbers occurring in A137822 : first differences of numbers n such that 3 | sum( Catalan(k), k=1..2n).

1, 2, 3, 7, 8, 21, 61, 62, 183, 547, 548, 1641, 4921, 4922, 14763, 44287, 44288, 132861, 398581, 398582, 1195743, 3587227, 3587228, 10761681, 32285041, 32285042, 96855123, 290565367, 290565368, 871696101, 2615088301, 2615088302

Offset: 1

Author

M. F. Hasler, May 15 2008

Keywords

• nonn
• easy

Comments

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.

The (very simple) sequence A137824 gives the index of A137822 at which A137823(n) occurs for the first time.

Crossrefs

Cf. A107755, A122983, A137821-A137824.

Programs

PARI

A137823(n) = (n%3==2)+3^((n-1)*2\3+1)\4+1