A076643 Positive integers read backwards, but omit a number if it is <= an earlier number.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 21, 31, 41, 51, 61, 71, 81, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 201, 301, 401, 501, 601, 701, 801, 901, 911, 921, 931, 941, 951, 961, 971, 981, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1001, 2001, 3001, 4001, 5001, 6001, 7001

Offset

1,2

Comments

a(n+1) - a(n) is a power of 10 or 2 if a(n) is of the form 10^m - 1. - David A. Corneth, Nov 26 2018

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

a((9*m^2 + 7*m + 2) / 2) = 10^m - 1, m > 0. - David A. Corneth, Nov 25 2018

Example

The beginning list is 1,2,3,4,5,6,7,8,9,1,11; but 1 < 9 so omit it.

Maple

d := N->`if`(N=0, [0], ListTools[Reverse](convert(N, base, 10))); a := N->sum(d(N)[n]*10^(n-1), n=1..nops(d(N))); dropsort := proc(S)::list; description "Forms a strictly increasing list by dropping terms."; local T, V; T := k->max(seq(S[j], j=1..k)); V := ListTools[MakeUnique]([seq(T(j), j=1..nops(S))]); return(V); end proc; dropsort([seq(a(n), n=1..2000)]);

Mathematica

Union@ FoldList[Max, IntegerReverse@ Range@ 1007] (* Michael De Vlieger, Nov 25 2018 *)

Prog

(PARI) nxt(n) = {my(d = digits(n), i = 1); while(i <= #d && d[i] == 9, i++); if(i <= #d, n+10^(#d-i), n+2)}
first(n) = my(res = vector(n)); res[1] = 1; for(i = 2, n, res[i] = nxt(res[i-1])); res \\ David A. Corneth, Nov 25 2018

Crossrefs

Cf. A004086.

Sequence in context: A096106 A321990 A076641 * A352463 A326402 A127204

Adjacent sequences: A076640 A076641 A076642 * A076644 A076645 A076646

Keyword

nonn,easy,look,base

Author

Francois Jooste (phukraut(AT)hotmail.com), Oct 23 2002

Status

approved