

A166508


Hypercomma numbers: n occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k1])+first_digit(S[k]) for each "legal" splitting n=concat(S[0],S[1]).


4



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 109, 806, 1023, 1044, 2005, 2676, 3066, 3602, 4051, 6053, 6246, 8011, 8349, 9427, 10022, 10074, 10587, 13090, 15031, 16867, 20088, 20699, 21698, 23108, 29986, 30091, 30306, 32226, 40022
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OFFSET

1,2


COMMENTS

This subsequence of A166511 consists of the numbers which occur as term in the sequence S(a,b), defined by S[0]=a, S[1]=b, S[k+1]=S[k]+10*last_digit(S[k1])+first_digit(S[k]), for any legal splitting n=concat(a,b).
"Legal" means that a and b have at least one digit each, and b has no leading zero(s) (unless b=0). See A166511 and A166512 for more information.
They are called hypercomma numbers because they are kcomma numbers (cf. A166507) with k as large as possible for the given number of (zero and nonzero) digits, or "phoenix" numbers because they can be cut into (two) pieces is any (legal) way and will be "reborn" as a whole out of the "pieces".


LINKS

Table of n, a(n) for n=1..47.
E. Angelini, kcomma numbers, Oct. 2009.
E. Angelini, kcomma numbers [Cached copy, with permission]


EXAMPLE

There is no legal way to split the singledigit numbers 1...9, therefore they are included.
More generally, a kcomma number which has exactly k nonzero digits when the last digit is ignored, will be in this sequence: e.g., 2005 can only be cut as (200,5); 10022 can only be cut as (1002,2) and (100,22), and it is a 2comma number (A166512).


PROG

(PARI) {for(n=1, 1e5, /*is_A166508(n)=*/ n%100 & for(d=1, #Str(n)1, my( a=n\10^d, b=n%10^d ); b<10^(d1) & d>1 & next /* not legal */; while(n > b=10*(a%10)+b\10^(#Str(b)1)+a=b, ); b>n & next(2) /* bad */); print1(n", "))}


CROSSREFS

Cf. A166507, A166511, A166512, A166513.
Sequence in context: A037124 A273737 A201982 * A223080 A248651 A306361
Adjacent sequences: A166505 A166506 A166507 * A166509 A166510 A166511


KEYWORD

base,nonn,changed


AUTHOR

Eric Angelini and M. F. Hasler, Oct 29 2009


STATUS

approved



