A064810 Self-locating strings within Pi: numbers n such that the string n is at position n in the decimal digits of Pi, where 1 is the 0th digit.

6, 27, 13598, 43611, 24643510, 71683711, 78714901, 268561754, 4261759184, 82638677082, 548535559133, 8773143366618

Offset

1,1

Comments

Near-misses '04658726522' and '0769960191236' occur at positions 4658726522 and 769960191236, respectively. - Kang Seonghoon, Nov 02 2020

a(13) > 5 * 10^13. - Kang Seonghoon, Nov 02 2020

Links

Table of n, a(n) for n=1..12.

Dave Andersen, The Pi-Search Page.

Tom Crawford and Brady Haran, Strings and Loops within Pi, Numberphile video (2020).

Brady Haran and Katie Steckles, 27 the Favourite Number, Numberphile video (2012).

Timothy Mullican, 50 trillion digits of pi (2020).

L. Brandon Stone, 27 and the Number Pi.

Example

6 is the first term because Pi is 3.1415926... and the digit 6 is in position 6 after the decimal point when the first 1 after the decimal point is considered to be at position 0.

Mathematica

Do[If[RealDigits[Pi, 10, a=i+IntegerLength@i-1, -2][[1, i;; a]]==IntegerDigits@i, Print@i], {i, 50000}] (* Giorgos Kalogeropoulos, Feb 21 2020 *)

Prog

(Python)
# download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
with open('pi-billion.txt', 'r') as f: digits_of_pi = f.readline()[2:]
# from sympy import S, isprime
# digits_of_pi = str(S.Pi.n(3*10**5))[2:] # alternate to loading data
def afind():
    global digits_of_pi
    for k in range(len(digits_of_pi)):
        s = str(k)
        if digits_of_pi[k:k+len(s)] == s: print(k, end=", ")
afind() # Michael S. Branicky, Jun 27 2021

Crossrefs

Cf. A000796, A057679, A057680.

Sequence in context: A048436 A276412 A006174 * A101454 A091911 A215896

Adjacent sequences: A064807 A064808 A064809 * A064811 A064812 A064813

Keyword

base,nonn,more

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 22 2001

Extensions

a(6)-a(10) from Alan Eliasen, May 11 2013

a(11) from Alan Eliasen, May 28 2013

a(12) added and name clarified by Kang Seonghoon, Nov 02 2020

Error in a(11) reported by Sergey Prokudin, edited by Robert Price, Mar 14 2022

Status

approved