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
Links
- Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Programs
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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
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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.
Comments