A260107 Lexicographically first increasing sequence of positive integers such that there are exactly a(k) terms less than or equal to 3*a(k), for each k.

1, 4, 5, 6, 13, 16, 19, 20, 21, 22, 23, 24, 25, 40, 41, 42, 49, 50, 51, 58, 61, 64, 67, 70, 73, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 121, 124, 127, 128, 129, 130, 131, 132, 133, 148, 151, 154, 155, 156, 157, 158, 159, 160, 175, 176

Offset

1,2

Comments

See A130011 and A260139 for other variants of this self-describing sequence.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Formula

a(n) <= 3n-2, and there are infinitely many indices (namely, all those of the form n = a(k)+1 for some k) for which equality holds.

Maple

l:=[1, 4]:for n from 2 to 20 do for j from l[n-1]+1 to `if`(n=2, l[n]-1, l[n]) do l:=[op(l), max(3*l[n-1], op(l))+1]: od: od: l; # Nathaniel Johnston, Apr 27 2011

Prog

(PARI) a=vector(100, i, 1); i=v=1; for(k=2, #a, if(k>a[i], v=3*a[i]; i++); a[k]=v++)

Crossrefs

Cf. A130011, A037988, A094591.

Sequence in context: A089119 A384192 A063833 * A167434 A139061 A029645

Adjacent sequences: A260104 A260105 A260106 * A260108 A260109 A260110

Keyword

nonn,easy

Author

M. F. Hasler, Jul 16 2015

Status

approved