A156147 a(n+1) = round( c(n)/2 ), where c(n) is the concatenation of all preceding terms a(1)...a(n) and a(1)=1.

1, 1, 6, 58, 5829, 58292915, 5829291479146458, 58292914791464577914645739573229, 5829291479146457791464573957322929146457395732288957322869786615

Offset: 1

Author

Eric Angelini, Alois P. Heinz, Farideh Firoozbakht and M. F. Hasler, Feb 04 2009

Keywords

• base
• easy
• nonn

Comments

Originally, round( c/2 ) was formulated as "rank of c in the sequence of odd resp. even (positive) numbers".

The sequence has some characteristics reminiscent of Thue-Morse type sequences. It "converges" to a non-periodic sequence of digits: all but the last digit of a given term will remain the initial digits of all subsequent terms. - M. F. Hasler

It's interesting that the number of digits of a(k) for k>2 equals to 2^(k-3). - Farideh Firoozbakht

Links

• M. F. Hasler et al., Table of n, a(n) for n = 1..12
• E. Angelini, Rang dans les Pairs/Impairs
• E. Angelini, Rang dans les Pairs/Impairs [Cached copy, with permission]
• E. Angelini et al., Rank of n in the Odd/Even sequence and follow-up messages on the SeqFan list, Feb 03 2009

Crossrefs

Cf. A156146 (other starting values).

Programs

Maple

rank:= n-> `if`(irem(n,2)=0, n/2, (n+1)/2): a:= proc(n) option remember; if n=1 then 1 else rank(parse(cat(seq(a(j), j=1..n-1)))) fi end: seq(a(n), n=1..10);  # Alois P. Heinz

Mathematica

a[1]=1; a[n_]:=a[n]=(v={};Do[v= Join[v,IntegerDigits[a[k]]],{k,n-1}]; Floor[(1+FromDigits[v])/2]) (* Farideh Firoozbakht *)

PARI

A156147(n)={local(a=1,t=1); while(n-->1,t=round(1/2*a=eval(Str(a,t))));t} /* M. F. Hasler */

Extensions

Typos fixed by Charles R Greathouse IV, Oct 28 2009