OFFSET
1,1
COMMENTS
A comma number n as defined in A166511 is the concatenation of numbers a,b (no leading zeros allowed) which occurs ("again") in the sequence S = S(a,b) defined by S[0]=a, S[1]=b, S[k+1] = S[k] + 10*last_digit(S[k-1]) + first_digit(S[n]).
Here we list the subsequence of numbers that can be split up in 2 different ways, n=concat(a,b)=concat(c,d), such that S(a,b) and S(c,d) both contain n.
Since the 4-digit terms remind of year numbers, the terminology of bicommatile (in analogy with bissextile) years has been introduced (as a joke).
LINKS
E. Angelini, Comma numbers, SeqFan mailing list, Oct 15 2009
E. Angelini, k-comma numbers, Oct. 2009.
E. Angelini, k-comma numbers [Cached copy, with permission]
EXAMPLE
None of the 3-digit terms in A166511 can be split up in 2 ways such that S(a,bc) and S(ab,c) both contain n=abc (concatenation, not product).
Therefore the smallest term in this sequence is a(1)=1023, which occurs in the sequences S(102,3) and S(10,23).
PROG
(PARI) {for(n=1, 1e4, /*is_A166512(n)=*/ my(c=2); for(d=1, #Str(n)-1, 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,easy,nonn
AUTHOR
Eric Angelini and M. F. Hasler, Oct 28 2009
STATUS
approved