A104781 -id:A104781 - cp's OEIS frontend

A109407 In decimal expansion of Pi, positions of ends of minimal sublists each containing all decimal digits at least once.

33, 51, 70, 97, 112, 139, 182, 210, 246, 289, 306, 329, 347, 363, 406, 450, 472, 506, 528, 551, 582, 601, 637, 666, 688, 705, 740, 758, 793, 852, 895, 918, 995, 1016, 1076, 1118, 1156, 1193, 1229, 1272, 1300, 1321, 1341, 1367, 1407, 1433, 1450, 1488, 1512

Offset: 1

Zak Seidov, Jun 27 2005

Essentially accumulating sums in A104781, but simpler Mmca code.

Cf. A104781.

p=RealDigits[N[Pi, 10000]][[1]];r=Range[0, 9];bb={};s={};Do[AppendTo[s, p[[i]]];If[Complement[r, s]== {}, AppendTo[bb, i];s={}], {i, 1, 10000}];A109407=bb

A277135 Separate the digits of Pi into smallest blocks such that each block contains all digits from 0 to 9. Sequence gives the last digits of blocks from left to right.

Original entry on oeis.org

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

Offset: 1

Bobby Jacobs, Oct 01 2016

			The first substring of Pi containing all 10 digits is 3.14159265358979323846264338327950, so a(1) = 0.
The next substring of Pi is 288419716939937510, so a(2) = 0.
The next substring of Pi is 5820974944592307816, so a(3) = 6.
The next substring of Pi is 406286208998628034825342117, so a(4) = 7.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A000796, A104781, A109407, A277140.

A277140 Earliest substring of the decimal expansion of Pi containing any of the 10 decimal digits at least once and disjoint from all earlier such substrings.

Original entry on oeis.org

314159265358979323846264338327950, 288419716939937510, 5820974944592307816, 406286208998628034825342117, 67982148086513, 282306647093844609550582231, 7253594081284811174502841027019385211055596, 4462294895493038196442881097, 566593344612847564823378678316527120, 1909145648566923460348610454326648213393607

Offset: 1

Bobby Jacobs, Oct 01 2016

Substrings can start with 0. For example, a(5) = 067982148086513.

			The first substring of Pi containing all 10 digits is 314159265358979323846264338327950.
The next substring of Pi is 288419716939937510.
The next substring of Pi is 5820974944592307816.
The next substring of Pi is 406286208998628034825342117.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A000796, A104781, A109407, A277135.

pi = RealDigits[Pi, 10, 300][[1]]; f := Block[{k = 10}, While[ Union[ Take[pi, k]] != Range[0, 9], k++]; a = Take[pi, k]; pi = Drop[pi, k]; FromDigits@ a]; lst = {}; Do[ AppendTo[lst, f], {10}]; lst (* Robert G. Wilson v, Nov 17 2016 *)

Definition clarified by Felix Fröhlich, Oct 30 2016

A104790 Lengths of the sections of decimal expansion of exp(Pi) containing all 10 digits at least once.

Original entry on oeis.org

25, 17, 40, 29, 26, 23, 22, 31, 30, 27, 31, 28, 31, 20, 13, 24, 17, 30, 37, 39, 30, 24, 28, 40, 20, 44, 32, 21, 18, 19, 18, 65, 26, 20, 24, 51, 25, 35, 37, 23, 39, 23, 20, 32, 25, 28, 16, 33, 20, 34, 44, 41, 32, 21, 31, 43, 17, 33, 17, 30, 44, 35, 36, 45, 19, 13, 36, 24, 17

Offset: 1

Zak Seidov, Mar 25 2005

Among first 500 sections, s483 has the minimal length=12. In general, in decimal expansion of exp(pi), the first three partitions of 10 distinct digits, are: p[12186]={8,4,2,7,0,3,5,6,9,1}, p[13451]={0,7,9,5,3,4,1,6,2,8}, p[15422]={0,2,9,1,3,8,7,5,6,4}.

			s1={2,3,1,4,0,6,9,2,6,3,2,7,7,9,2,6,9,0,0,5,7,2,9,0,8}-25 digits,
s2={6,3,6,7,9,4,8,5,4,7,3,8,0,2,6,6,1}-17 digits,
s3={2,3,1,4,0,6,9,2,6,3,2,7,7,9,2,6,9,0,0,5,7,2,9,0,8}-40 digits,
s483={4,7,8,1,3,5,6,6,2,4,0,9}- 12 digits.

Cf. A039661, A104781.

A104791 In decimal expansion of exp(Pi), positions of 10-digit partitions containing exactly 10 distinct digits.

Original entry on oeis.org

12186, 13451, 15422, 27621, 27622, 32790, 33051, 35249, 38760

Offset: 1

Zak Seidov, Mar 25 2005

			p[ 12186 ]= {8 4 2 7 0 3 5 6 9 1},
p[ 13451 ]= {0 7 9 5 3 4 1 6 2 8},
p[ 15422 ]= {0 2 9 1 3 8 7 5 6 4},
p[ 27621 ]= {9 3 2 5 8 4 1 0 7 6},
p[ 27622 ]= {3 2 5 8 4 1 0 7 6 9},
p[ 32790 ]= {2 4 0 8 6 5 3 7 1 9},
p[ 33051 ]= {6 2 5 3 9 0 4 1 8 7},
p[ 35249 ]= {6 3 7 2 5 8 9 4 0 1},
p[ 38760 ]= {3 1 0 6 9 2 5 4 7 8}.

Cf. A039661, A104781, A104790.

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A109407 In decimal expansion of Pi, positions of ends of minimal sublists each containing all decimal digits at least once.

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A277135 Separate the digits of Pi into smallest blocks such that each block contains all digits from 0 to 9. Sequence gives the last digits of blocks from left to right.

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A277140 Earliest substring of the decimal expansion of Pi containing any of the 10 decimal digits at least once and disjoint from all earlier such substrings.

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A104790 Lengths of the sections of decimal expansion of exp(Pi) containing all 10 digits at least once.

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A104791 In decimal expansion of exp(Pi), positions of 10-digit partitions containing exactly 10 distinct digits.

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