A257350 a(n+1) = a(n) + smallest nonzero (and unused) integer embedded in a(n) as a (not necessarily contiguous) subchain.

1, 2, 4, 8, 16, 22, 44, 88, 176, 183, 186, 202, 222, 444, 888, 1776, 1793, 1802, 1812, 1823, 1835, 1840, 1854, 1869, 1887, 1974, 1993, 2006, 2032, 2055, 2080, 2108, 2129, 2158, 2216, 2432, 2456, 2501, 2551, 2602, 2662, 2724, 2751, 2822, 2904, 2994, 3088, 3118

Offset

1,2

Comments

The subchain numbers used are: 0, 1, 2, 4, 8, 6, 22, 44, 88, 7, 3, 16, 20, 222, 444, 888, 17, 9, 10, 11, 12, 5, 14, 15, 18, 87, 19, 13, 26, 23, 25, 28, 21, 29, ...

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100000

Example

After 186, the next term can be any of 186 + {1,8,6,18,16,86,186}, and 16 is the smallest of these that has not yet been used, so the next term is 186+16 = 202.

Mathematica

f[n_] := Block[{used = {0}, s = Table[1, {n}], k}, For[k = 2, k <= n, k++, s[[k]] = s[[k - 1]] + SelectFirst[ FromDigits /@ Rest@ DeleteDuplicates@ Sort@ Subsets@ IntegerDigits@ s[[k - 1]], ! MemberQ[used, #] &]; AppendTo[used, s[[k]] - s[[k - 1]]] ]; s ]; f@36. (* If you want to see the "used" data as well, replace the "s" near the end of the function with "{s, used}" *)

Crossrefs

A variant of A257165.

Sequence in context: A230102 A063108 A161140 * A257165 A262224 A058961

Adjacent sequences: A257347 A257348 A257349 * A257351 A257352 A257353

Keyword

nonn,base

Author

Jean-Marc Falcoz, Apr 17 2015 and Michael De Vlieger, Apr 19 2015

Extensions

a(35)-a(48) from Hiroaki Yamanouchi, May 03 2015

Status

approved