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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
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
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
KEYWORD
base,nonn
AUTHOR
Eric Angelini and M. F. Hasler, Oct 29 2009
STATUS
approved