A358168 First n-digit number to occur in Van Eck's Sequence (A181391).

0, 14, 131, 1024, 10381, 100881, 1014748, 10001558, 100246289, 1000943528, 10010107437

Offset: 1

Author

G. L. Honaker, Jr., Nov 01 2022

Keywords

• nonn
• base
• hard
• more

Comments

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

Examples

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

Crossrefs

Cf. A181391, A358180.

Programs

Mathematica

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 *)

Python

from itertools import count
def A358168(n):
    b, bdict, k = 0, {0:(1,)},10**(n-1) if n > 1 else 0
    for m in count(2):
        if b >= k:
            return b
        if len(l := bdict[b]) > 1:
            b = m-1-l[-2]
            if b in bdict:
                bdict[b] = (bdict[b][-1],m)
            else:
                bdict[b] = (m,)
        else:
            b = 0
            bdict[0] = (bdict[0][-1],m) # Chai Wah Wu, Nov 05 2022

Extensions

a(8)-a(10) from Chai Wah Wu, Nov 05 2022

a(11) from Martin Ehrenstein, Nov 05 2022