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

Author

M. F. Hasler, Jul 16 2015

Keywords

• nonn
• easy

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

Crossrefs

Cf. A130011, A037988, A094591.

Programs

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

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++)

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.