A280631 Starting position (after the decimal point) of the first n-digit palindrome in the decimal expansion of Pi.

0, 24, 1, 43, 19, 762, 640, 3732, 6577, 16061, 247146, 273840, 879326, 5380812, 10593200, 171880711, 105176740, 517694394, 559015193, 824827924

Offset

1,2

Comments

The first 10-digit palindrome in the decimal expansion of Pi (0136776310) first appears at a palindromic position (16061).

Links

Table of n, a(n) for n=1..20.

Example

a(2) = 24 because the first 2-digit palindrome in the decimal expansion of Pi (33) starts 24 digits after the decimal point.
3.14159265358979323846264(33)...

Mathematica

With[{d = First@ RealDigits@ N[Pi, 10^6]}, Prepend[DeleteCases[Rest@ #, 0], First@ #] &@ Flatten@ Map[If[Length@ # == 0, 0, #[[1, 1]] - 1] &@ SequencePosition[d, #] &, Table[If[Length@ # == 0, {}, First@ #] &@ Select[Partition[d, n, 1], # == Reverse@ # &], {n, 20}]]] (* Michael De Vlieger, Jan 07 2017, Version 10.1 *)

Prog

(Python)
from sympy import S
# download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
# with open('pi-billion.txt', 'r') as f: pi_digits = f.readline()
pi_digits = str(S.Pi.n(3*10**5+2))[:-2] # alternative to above
pi_digits = pi_digits.replace(".", "")
def ispal(s): return s == s[::-1]
def a(n):
    for idx in range(len(pi_digits)-n):
        if ispal(pi_digits[idx:idx+n]):
            return int(pi_digits[idx:idx+n]), idx
    return None, None # Not found: Increase number of digits
print([a(n)[1] for n in range(1, 13)]) # Michael S. Branicky, Jan 10 2022

Crossrefs

Cf. A000796, A002113, A279885.

Sequence in context: A040598 A097190 A103903 * A040599 A076721 A232988

Adjacent sequences: A280628 A280629 A280630 * A280632 A280633 A280634

Keyword

nonn,base,more,less

Author

Bobby Jacobs, Jan 06 2017

Extensions

a(14)-a(15) from Michael De Vlieger, Jan 07 2017

a(16)-a(20) from Michael S. Branicky, Jan 10 2022

Status

approved