A358168 - OEIS

%I #30 Nov 06 2022 01:40:20

%S 0,14,131,1024,10381,100881,1014748,10001558,100246289,1000943528,

%T 10010107437

%N First n-digit number to occur in Van Eck's Sequence (A181391).

%C a(6)-a(7) from Chuck Gaydos.

%e a(2) = 14 because 14 is the first 2-digit number occurring in A181391.

%t nn = 2^20; q[_] = False; q[0] = True; a[_] = 0; c[_] = -1; c[0] = 2; m = 1; {0}~Join~Rest@ Reap[Do[j = c[m]; a[n] = m; c[m] = n; m = 0; If[j > 0, m = n - j]; If[! q[#2], Sow[#1]; q[#2] = True] & @@ {a[n], IntegerLength[a[n]]}, {n, 3, nn}] ][[-1, -1]] (* _Michael De Vlieger_, Nov 05 2022 *)

%o (Python)

%o from itertools import count

%o def A358168(n):

%o     b, bdict, k = 0, {0:(1,)},10**(n-1) if n > 1 else 0

%o     for m in count(2):

%o         if b >= k:

%o             return b

%o         if len(l := bdict[b]) > 1:

%o             b = m-1-l[-2]

%o             if b in bdict:

%o                 bdict[b] = (bdict[b][-1],m)

%o             else:

%o                 bdict[b] = (m,)

%o         else:

%o             b = 0

%o             bdict[0] = (bdict[0][-1],m) # _Chai Wah Wu_, Nov 05 2022

%Y Cf. A181391, A358180.

%K nonn,base,hard,more

%O 1,2

%A _G. L. Honaker, Jr._, Nov 01 2022

%E a(8)-a(10) from _Chai Wah Wu_, Nov 05 2022

%E a(11) from _Martin Ehrenstein_, Nov 05 2022