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Position of the first time an n-digit number appears twice in a row after the decimal point of e.
2

%I #40 Jan 21 2023 02:00:29

%S 31,49,97,2,112869,5005575,1561314,69682897,1841794338

%N Position of the first time an n-digit number appears twice in a row after the decimal point of e.

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

%e a(1) = 31 because the first time a 1-digit number appears twice in a row in the decimal expansion of e is 31 digits after the decimal point: 2.718281828459045235360287471352(66)...

%t s = First@ RealDigits[E, 10, 51*^5]; Table[p = Partition[s, k, 1];

%t SelectFirst[ Range[ Length[p] - k], p[[#]] == p[[# + k]] &] - 1, {k, 7}] (* _Giovanni Resta_, Sep 05 2017 *)

%Y Cf. A001113, A287994, A290984.

%K nonn,base,more

%O 1,1

%A _Bobby Jacobs_, Sep 01 2017

%E a(6)-a(8) from _Giovanni Resta_, Sep 05 2017

%E a(9) from _Michael S. Branicky_, Jan 20 2023