A123483 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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

a(68322765) = 35, a(68322653) = 39, a(24115250) = 44, a(16078940) = 70, a(68322589) = 95. Other numbers in the above list have not appeared after 6*10^8 terms. - Scott R. Shannon, Feb 26 2026

LINKS

Franklin T. Adams-Watters, The first 10000 terms

Nick Hobson, Python program for this sequence

CROSSREFS

Cf. A005132.

Sequence in context: A365781 A298400 A070295 * A320577 A199805 A053248

Adjacent sequences: A123480 A123481 A123482 * A123484 A123485 A123486

KEYWORD

nonn,look

AUTHOR

Franklin T. Adams-Watters, Sep 28 2006

STATUS

approved