A086639 -id:A086639 - cp's OEIS frontend

A090897 Next n digits of Pi.

3, 14, 159, 2653, 58979, 323846, 2643383, 27950288, 419716939, 9375105820, 97494459230, 781640628620, 8998628034825, 34211706798214, 808651328230664, 7093844609550582, 23172535940812848, 111745028410270193, 8521105559644622948, 95493038196442881097

Offset: 1

Michael Joseph Halm, Feb 26 2004

More precisely: the integer resulting from reading the "next n digits of Pi" in base 10, so leading zeros cannot be directly seen, but easily be "reconstructed" from the fact that the term will have less than n digits although it is made from n digits of Pi. - M. F. Hasler, Jan 06 2023

It seems that all terms have at least one prime factor that does not appear in the combined list of prime factors of the preceding terms of the sequence. - Mario Cortés, Aug 20 2020 [Checked up to n=65. - Michel Marcus, Aug 21 2020]

			a(3) = 159 because after the first (a(1) = 3) and the next two digits of Pi (a(2) = 14) the next three are 159.
From _Aaron T Cowan_, Jan 03 2023: (Start)
Other examples are as follows and fall into a triangular digit pattern, though there is no guarantee that they will remain triangular in all cases
  a(1) = 3;
  a(2) = 14;
  a(3) = 159;
  a(4) = 2653;
  a(5) = 58979;
   (End)
Indeed, precisely whenever A086639(n) = 0, then the corresponding term of this sequence will lack one or more leading zeros and therefore the above list will deviate from the triangular shape. - _M. F. Hasler_, Jan 06 2023

Michel Marcus, Table of n, a(n) for n = 1..100

Cf. A000796 (Pi), A016062, A081368, A086639.

Partitioner := proc(cons, len) local i, R, spl; R := []; i:=0;
spl := L -> [seq([seq(L[i], i=1 + n*(n+1)/2..(n+1)*(n+2)/2)], n=0..len)]:
ListTools:-Reverse(convert(floor(cons*10^((len+1)*(len+2)/2)), base, 10)):
map(`@`(parse, cat, op), spl(%)) end:
aList := -> Partitioner(Pi, 20); aList(20); # Peter Luschny, Aug 22 2020

With[{pi=RealDigits[Pi,10,500][[1]]},FromDigits/@Table[Take[pi,{n (n-1)/2+1, (n(n+1))/2}],{n,25}]] (* Harvey P. Dale, Dec 24 2011 *)

lista(nn) = {my(nd = 5+nn*(nn+1)/2); default(realprecision, nd); my(vd = digits(floor(Pi*10^nd))); my(pos = 1); my(vr = vector(nn)); for (n=1, nn, vr[n] = fromdigits(vector(n, k, vd[k+ pos-1])); pos += n;); vr;} \\ Michel Marcus, Aug 21 2020

a(n) = floor( Pi * 10^(n*(n+1)/2-1) ) mod (10^n). - Carl R. White, Aug 13 2010

A083437 Write decimal expansion of Pi in triangular form; sequence gives right edge.

Original entry on oeis.org

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

Offset: 1

Cino Hilliard, Jul 24 2003

Select digits from decimal expansion of Pi corresponding to triangular number indices. - Harvey P. Dale, Oct 15 2011

			Triangle is:
  3
  14
  159
  2653
  58979
  323846
  2643383
  27950288
  419716939
  9375105820

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000796, A086639.

pi = RealDigits[Pi, 10, 5565][[1]]; Table[ pi[[n(n + 1)/2]], {n, 1, 105}]
With[{nn=110},RealDigits[Pi,10,(nn(nn+1))/2][[1]][[Accumulate[ Range[ nn]]]]] (* Harvey P. Dale, Oct 15 2011 *)
Module[{nn=110},Last[#]&/@TakeList[RealDigits[Pi,10,(nn(nn+1))/2][[1]],Range[ nn]]] (* Harvey P. Dale, Oct 02 2022 *)

a(n) = A000796(2-n*(n+1)/2). - M. F. Hasler, Oct 20 2011

Edited by Robert G. Wilson v, Jul 26 2003

A086657 Write decimal expansion of e in triangular form; sequence gives right edge.

Original entry on oeis.org

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

Offset: 1

Cino Hilliard, Jul 27 2003

			Triangle is
2
71
828
1828
45904
523536
0287471
35266249
775724709
3699959574
96696762772
407663035354

Cf. A083437, A086639.

A086658 Write decimal expansion of e in triangular form; sequence gives left edge.

Original entry on oeis.org

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

Offset: 1

Cino Hilliard, Jul 27 2003

			Triangle is
2
71
828
1828
45904
523536
0287471
35266249
775724709
3699959574
96696762772
407663035354

Cf. A083437, A086639.

cp's OEIS Frontend

A090897 Next n digits of Pi.

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A083437 Write decimal expansion of Pi in triangular form; sequence gives right edge.

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A086657 Write decimal expansion of e in triangular form; sequence gives right edge.

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A086658 Write decimal expansion of e in triangular form; sequence gives left edge.

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Author

Keywords

Examples

Crossrefs