A316155 Numbers with additive persistence = 4 and digits in nondecreasing order.

19999999999999999999999, 28999999999999999999999, 37999999999999999999999, 38899999999999999999999, 46999999999999999999999, 47899999999999999999999, 48889999999999999999999, 55999999999999999999999, 56899999999999999999999, 57799999999999999999999, 57889999999999999999999

Offset

1,1

Comments

All terms of <= 32 digits have digit sum 199. - Robert Israel, Jun 25 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Additive Persistence

Formula

A031286(a(n)) = 4.

Example

Repeatedly taking the sum of digits starting with 19999999999999999999999 gives 199, 19, 10 and 1. There are four steps, so the additive persistence is 4 and 19999999999999999999999 is a member.

Maple

S:= proc(d, t, m) # d digits of sum t with max m
    option remember;
    local j;
  if d*m < t then return [] fi;
  if d = 1 then if t > 0 then return [[t]] else return [] fi fi;
  [seq(op(map(L -> [op(L), j], procname(d-1, t-j, j))), j=1..min(m, t))]
end proc:
seq(op(sort(map(t -> add(t[-i]*10^(i-1), i=1..nops(t)), S(d, 199, 9)))), d=23..24); # Robert Israel, Jun 25 2018

Crossrefs

Cf. A031286, A304366, A304367, A304368.

Sequence in context: A246254 A238360 A304373 * A216854 A008916 A292859

Adjacent sequences: A316152 A316153 A316154 * A316156 A316157 A316158

Keyword

nonn,base

Author

Jaroslav Krizek, Jun 25 2018

Status

approved