A260465 a(n) is the smallest number not already in the sequence such that a(n)^3 begins with n.

1, 3, 7, 16, 8, 4, 9, 2, 21, 10, 48, 5, 11, 52, 25, 55, 12, 57, 27, 59, 6, 61, 62, 29, 63, 64, 14, 66, 31, 67, 68, 32, 15, 70, 33, 154, 72, 73, 34, 74, 161, 35, 76, 164, 77, 36, 78, 169, 17, 37, 80, 174, 81, 38, 82, 178, 83, 18, 39, 182, 85, 184, 86, 40, 87, 188, 189, 19, 191, 89, 193, 90, 194, 42, 91, 197, 92, 199, 43

Offset: 1

Author

Derek Orr, Jul 26 2015

Keywords

• nonn
• base

Comments

Conjectured to be a permutation of the natural numbers.

Links

• Derek Orr, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A018852.

Programs

PARI

v=[]; k=1; while(#v<100, d=digits(k^3); D=digits(#v+1); if(#D<=#d, c=1; for(i=1, #D, if(D[i]!=d[i], c=0; break)); if(c&&!vecsearch(vecsort(v), k), v=concat(v, k); k=0)); k++); v

Formula

a(n) >= n^(1/3) for all n > 0. If a(n) = n^(1/3), then n is a cube. Note the converse is false: a(27) = 14.