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A166513
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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]).
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4
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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).
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PROG
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(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))}
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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