A123483 Second order Recamán's sequence: a(0) = 0; for n > 0, a(n) = a(n-1) - A005132(n) if that number is positive and not already in the sequence, otherwise a(n-1) + A005132(n).

0, 1, 4, 10, 8, 15, 2, 22, 34, 13, 24, 46, 36, 59, 50, 26, 18, 43, 86, 148, 106, 169, 128, 110, 68, 51, 94, 78, 122, 107, 62, 48, 94, 173, 60, 138, 252, 175, 136, 58, 20, 99, 136, 56, 92, 11, 46, 128, 162, 79, 112, 28, 60, 145, 114, 200, 170, 83, 54, 142, 170, 81, 108, 198

Offset: 0

Author

Franklin T. Adams-Watters, Sep 28 2006

Keywords

• nonn

Comments

I conjecture that this sequence contains every natural number. (Even though through n=10000, we still haven't seen 3; we are still occasionally seeing small numbers.) This sequence has an interesting graph.

The smallest n such that a(n) = 3, 6, 12 are, respectively, 4729925, 5808155, 2093396. The following numbers less than 100 do not appear in the sequence for n <= 10^7: 7, 17, 19, 21, 23, 25, 27, 29, 35, 39, 41, 44, 45, 57, 61, 65, 67, 70, 71, 73, 77, 87, 91, 95. - Nick Hobson, Feb 18 2007

Links

• Franklin T. Adams-Watters, The first 10000 terms
• Nick Hobson, Python program for this sequence

Crossrefs

Cf. A005132.