cp's OEIS Frontend

A282171 Single-digit numbers in the order in which they first appear in the decimal expansion of e, followed by the two-digit numbers in the order in which they appear, then the three-digit numbers, and so on.

%I A282171 #50 Jun 08 2017 16:33:48
%S A282171 2,7,1,8,4,5,9,0,3,6,27,71,18,82,28,81,84,45,59,90,52,23,35,53,36,60,
%T A282171 87,74,47,13,26,66,62,24,49,97,77,75,57,72,70,93,69,99,95,96,67,76,40,
%U A282171 63,30,54,94,38,21,17,78,85,25,51,16,64,42,46,39,91,19
%N A282171 Single-digit numbers in the order in which they first appear in the decimal expansion of e, followed by the two-digit numbers in the order in which they appear, then the three-digit numbers, and so on.
%C A282171 Note that (except for 0 itself), numbers may not begin with 0. So that when we reach ...459045..., this contributes 90 to the sequence but not "04". - _N. J. A. Sloane_, Feb 08 2017
%H A282171 Michael De Vlieger, <a href="/A282171/b282171.txt">Table of n, a(n) for n = 1..10000</a>
%e A282171 From _Michael De Vlieger_, Feb 09 2017: (Start)
%e A282171 Consider the decimal expansion of e=2.718281828459045235360...
%e A282171 The first 4 terms are 2,7,1,8 since these single digits appear in that order above. We do not encounter a different digit till we reach 4,5,9,0, thus these follow the first four in the sequence. We encounter 3 next, and finally 6 and have found all the single digits in the expansion.
%e A282171 a(11)=27 because we find the two-digit group "27" first, followed by a(12)=71, etc. until we exhaust the 90 possible two-digit groups that do not start with a zero.
%e A282171 a(101)=271 because we find the three-digit group "271" first, followed by a(102)=718, etc. until we exhaust the 900 possible 3-digit groups that do not have leading zeros, etc. (End)
%t A282171 e = First@ RealDigits@ N[E, 10^6]; MapIndexed[10^(First@ #2 - 1) - 1 - Boole[First@ #2 == 1] + Flatten@ Values@ KeySort@ PositionIndex@ #1 &, Table[SequencePosition[e, IntegerDigits@ k][[1, 1]], {n, 4}, {k, If[n == 1, 0, 10^(n - 1)], 10^n - 1}]] (* _Michael De Vlieger_, Feb 09 2017, Version 10.1 *)
%Y A282171 Cf. A001113, A105177 (analog for Pi), A105178.
%K A282171 nonn,base,look
%O A282171 1,1
%A A282171 _Bobby Jacobs_, Feb 07 2017
%E A282171 Edited by _N. J. A. Sloane_, Feb 08 2017
%E A282171 a(5), a(6), a(9), and a(10) inserted by _Bobby Jacobs_, Feb 09 2017
%E A282171 More terms from _Michael De Vlieger_, Feb 09 2017