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

Author

Michael Joseph Halm, Feb 26 2004

Keywords

• easy
• nonn
• base

Comments

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]

Examples

			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
		

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

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 *)

PARI

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

Formula

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