A290984 First n-digit number to appear twice in a row in the decimal expansion of e.

6, 95, 427, 1828, 34619, 507629, 7342911, 21958718, 852480872

Offset: 1

Author

Bobby Jacobs, Aug 16 2017

Keywords

• base
• more
• nonn

Comments

18281828 appears in e before any 1-digit, 2-digit, or 3-digit number appears twice in a row.

a(n) starts at positions 31, 49, 97, 2, 112869, 5005575, 1561314, 69682897, ... - Bobby Jacobs, Sep 05 2017

Examples

			a(1) = 6 because 6 is the first 1-digit number to appear twice in a row in the decimal expansion of e = 2.718281828459045235360287471352(66)...
		

Crossrefs

Cf. A001113, A288291, A290977.

Programs

Mathematica

With[{s = Rest@ First@ RealDigits[N[E, 10^5]]}, Keys@ Merge[#, Identity] &@ Table[TakeSmallest[#, 1] &@ Sort[Map[#[[1, 1]] &, DeleteCases[#, {}]]] &@ Map[SequenceCases[#, {a_, b_} /; b == a + n] &, KeyMap[FromDigits, PositionIndex@ Partition[s, n, 1]]], {n, 4}]] (* Michael De Vlieger, Aug 16 2017 *)
(* or *)
s = First@ RealDigits[E,10,51*^5]; Table[p = Partition[s, k, 1]; FromDigits @@ p[[ Select[ Range[ Length@p - k], p[[#]] == p[[#+k]] &, 1]]], {k, 7}] (* much faster, Giovanni Resta, Sep 05 2017 *)

Extensions

a(6)-a(8) from Giovanni Resta, Sep 05 2017

a(9) from Michael S. Branicky, Jan 20 2023