OFFSET
1,1
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
EXAMPLE
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)...
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 *)
CROSSREFS
KEYWORD
base,more,nonn
AUTHOR
Bobby Jacobs, Aug 16 2017
EXTENSIONS
a(6)-a(8) from Giovanni Resta, Sep 05 2017
a(9) from Michael S. Branicky, Jan 20 2023
STATUS
approved