A105177 -id:A105177 - cp's OEIS frontend

A321043 Single-digit numbers in the order in which they first appear in the decimal expansions of powers of 2, followed by the two-digit numbers in the order in which they appear, then the three-digit numbers, and so on.

1, 2, 4, 8, 6, 3, 5, 0, 9, 7, 16, 32, 64, 12, 28, 25, 56, 51, 10, 24, 20, 48, 40, 96, 81, 19, 92, 63, 38, 84, 27, 76, 68, 65, 55, 53, 36, 13, 31, 72, 26, 62, 21, 14, 44, 52, 42, 88, 85, 57, 97, 71, 15, 41, 94, 43, 30, 83, 86, 60, 67, 77, 33, 35, 54, 34, 17, 45

Offset: 1

David Williams, Oct 26 2018

Apparently this algorithm applied to most sequences will produce a fractal scatterplot graph. - David Williams, Jan 20 2019

			1,2,4,8,16,32,64,128,256,512,1024, ..., 4096, ..., 32768, ... gives 1,2,4,8,6,3,5,0,9,7.
Then we get 16,32,64,12,28,25,56,51,10,24,20,48,40,96,81,19,92,...
11 does not appear until 2^40 = 1099511627776.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A321043

Cf. A000079, A105177.

See A030000 for an inverse.

PARI
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Edited by N. J. A. Sloane, Oct 27 2018

More terms from Rémy Sigrist, Oct 27 2018

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.

Original entry on oeis.org

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, 87, 74, 47, 13, 26, 66, 62, 24, 49, 97, 77, 75, 57, 72, 70, 93, 69, 99, 95, 96, 67, 76, 40, 63, 30, 54, 94, 38, 21, 17, 78, 85, 25, 51, 16, 64, 42, 46, 39, 91, 19

Offset: 1

Bobby Jacobs, Feb 07 2017

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

			From _Michael De Vlieger_, Feb 09 2017: (Start)
Consider the decimal expansion of e=2.718281828459045235360...
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.
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.
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)

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A001113, A105177 (analog for Pi), A105178.

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 *)

Edited by N. J. A. Sloane, Feb 08 2017
a(5), a(6), a(9), and a(10) inserted by Bobby Jacobs, Feb 09 2017
More terms from Michael De Vlieger, Feb 09 2017

A171091 Digits in the order in which they appear in the fractional part of the decimal expansion of Pi.

Original entry on oeis.org

1, 4, 5, 9, 2, 6, 3, 8, 7, 0

Offset: 1

Jean-Yves BOULAY, Sep 07 2010

3,1,8,0,9,6,7,5,2,4 (see A049541) and 6,1,8,0,3,9,7,4,2,5 (see A094214) are the equivalent sequences for 1/Pi and 1/phi. Conjecture: These sequences are not random but are in ratio of 3/2 between the first six and last four digits and the first six digits and last four are the same.

David H. Bailey, The computation of pi to 29360000 decimal digits..., Math. Comp. 50 (1988) 283
Jean-Yves Boulay, Pi and Golden Number: not random occurrences of the ten digits
Eric W. Weisstein, Pi digits, MathWorld.

Cf. A000796, A105177

DeleteDuplicates[Rest[RealDigits[Pi,10,40][[1]]]] (* Harvey P. Dale, Jan 31 2020 *)

Edited by N. J. A. Sloane, Sep 08 2010

cp's OEIS Frontend

A321043 Single-digit numbers in the order in which they first appear in the decimal expansions of powers of 2, followed by the two-digit numbers in the order in which they appear, then the three-digit numbers, and so on.

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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.

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A171091 Digits in the order in which they appear in the fractional part of the decimal expansion of Pi.

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