A037024 Position of start of first occurrence of prime(n) after the decimal point in expansion of Pi.

6, 9, 4, 13, 94, 110, 95, 37, 16, 186, 137, 46, 2, 23, 119, 8, 4, 219, 98, 39, 299, 13, 26, 11, 12, 852, 3486, 1487, 206, 362, 297, 1096, 859, 525, 2606, 393, 1657, 1410, 1182, 428, 438, 728, 1944, 168, 37, 704, 93, 135, 484, 185, 229, 1688, 1707, 1713, 1006

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Dave Andersen, The Pi-Search Page

Example

Pi = 3.14159265358979323846264338327950288... (see A000796).
First occurrence of prime(23) = 83 starts at the 26th digit after the decimal point, hence a(23) = 26.

Prog

(Magma) k:=3500; R := RealField(k); [ Position(IntegerToString(Round(10^k*(-3 + Pi(R)))), IntegerToString(NthPrime(n))) : n in [1..55] ]; /* Klaus Brockhaus, Feb 15 2007 */
(Python)
from itertools import takewhile
from sympy import S, prime, primerange
# 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()[1:]
pi_digits = str(S.Pi.n(10**4))[1:] # alternative to above
def aupton(nn):
    plocs = (pi_digits.find(str(p)) for p in primerange(2, prime(nn)+1))
    return list(takewhile(lambda x: x>=0, plocs)) # until p not found
print(aupton(55)) # Michael S. Branicky, Jun 12 2021

Crossrefs

Cf. A000796, A014777.

Sequence in context: A021063 A216638 A110649 * A309343 A254276 A021939

Adjacent sequences: A037021 A037022 A037023 * A037025 A037026 A037027

Keyword

nonn,base

Author

Patrick De Geest, Jan 04 1999

Extensions

Edited by Klaus Brockhaus, Feb 15 2007

Status

approved