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A166513 3-comma numbers: n occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]) for three different splittings n=concat(S[0],S[1]). 4
2676, 6246, 8349, 9427, 10587, 11558, 11756, 11811, 12427, 12788, 13090, 13110, 14328, 15031, 15187, 15493, 15637, 16867, 18322, 18768, 19918, 20699, 21138, 21422, 21698, 22824, 23108, 23242, 23868, 24456, 24854, 25342, 25478, 26583 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This subsequence of A166512 consists of the numbers that can be split up in (at least) three different ways, n=concat(a,b)=concat(c,d)=concat(e,f), such that the sequences S(a,b), S(c,d) and S(e,f) all contain n.

(Here S(a,b) is the sequence defined by S[0]=a, S[1]=b, S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]).) See A166511 and A166512 for more information.

LINKS

Table of n, a(n) for n=1..34.

E. Angelini, k-comma numbers, Oct. 2009.

E. Angelini, k-comma numbers [Cached copy, with permission]

EXAMPLE

The 4-digit terms 2676, 6246, 8349, 9427 occurring in A166512, can be split up in any of the 3 possible ways such that S(a,bcd), S(ab,cd), and S(abc,d) all contain abcd (concatenation, not product). Therefore they are in this sequence, and they are even hypercomma (or "phoenix") numbers (A166508).

PROG

(PARI) {for(n=1e4, 1e5, /*is_A166513(n)=*/ my(c=3); for(d=1, #Str(n)-1, d+c>#Str(n) & break; my( a=n\10^d, b=n%10^d ); b<10^(d-1) & (d>1 | a%10==0) & next; while(n > b=10*(a%10)+b\10^(#Str(b)-1)+a=b, ); b==n & c--==0 & /*return(1)*/ !print1(n", ") & break))}

CROSSREFS

Cf. A166507, A166508, A166511, A166512.

Sequence in context: A112138 A345560 A345815 * A345569 A345825 A258505

Adjacent sequences:  A166510 A166511 A166512 * A166514 A166515 A166516

KEYWORD

base,nonn

AUTHOR

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

STATUS

approved

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Last modified July 25 10:05 EDT 2021. Contains 346289 sequences. (Running on oeis4.)