cp's OEIS Frontend

A166507 Least n-comma number: smallest nonnegative integer that occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]) for at least n different splittings a(n)=concat(S[0],S[1]).

%I A166507 #14 Nov 11 2019 00:35:14
%S A166507 0,10,1023,2676,16867,111688,1522828,11386882,112273999,1212143716,
%T A166507 11232152998,121321194596
%N A166507 Least n-comma number: smallest nonnegative integer that occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]) for at least n different splittings a(n)=concat(S[0],S[1]).
%C A166507 This subsequence of A166508 and of A166511 consists of the least numbers (= nonnegative integers) a(n) 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[k-1])+first_digit(S[k]), for at least n legal splittings a(n)=concat(a,b).
%C A166507 "Legal" means that a and b have at least one digit each, and b has no leading zero(s) (unless b=0). Therefore a(n) must have at least n nonzero digits preceding the last digit (cf. formula). See A166511 and A166512 for more information.
%H A166507 E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Commatile.htm">k-comma numbers</a>, Oct. 2009.
%H A166507 E. Angelini, <a href="/A166507/a166507.pdf">k-comma numbers</a> [Cached copy, with permission]
%F A166507 a(k) >= [10^k/9]*10 = (10^(k+1)-1)/9-1.
%e A166507 There are 0 ways to split a(0)=0 in two substrings, so this is the smallest 0-comma number.
%e A166507 The number a(1)=10 is the smallest 1-comma number, cf. A166511.
%e A166507 The number a(2)=1023 is the smallest 2-comma number: it occurs in S(10,23) and in S(102,3), cf. A166512.
%o A166507 (PARI) A166507(k) = { my(a,b,c); for( n=10^k\9*10,1e9, c=k; n%100 | next; for(d=1,#Str(n)-1, d+c>#Str(n) & break /* not possible: next n */; a=n\10^d, b=n%10^d; b<10^(d-1) & d>1 & next /* not legal: next d */; while(n > b=10*(a%10)+b\10^(#Str(b)-1)+a=b,); b>n & next; c-- | return(n)))}
%Y A166507 Cf. A166508, A166511, A166512, A166513.
%K A166507 base,hard,more,nonn
%O A166507 0,2
%A A166507 _Eric Angelini_ and _M. F. Hasler_, Oct 29 2009
%E A166507 a(6)-a(11) from _Lars Blomberg_, Jan 06 2015