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

Author

Patrick De Geest, Jan 04 1999

Keywords

• nonn
• base

Examples

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

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• Dave Andersen, The Pi-Search Page

Crossrefs

Cf. A000796, A014777.

Programs

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 */

Mathematica

Module[{p = Rest[First[RealDigits[Pi, 10, 10^4]]], n = 0, a}, Reap[While[(a = SequencePosition[p, IntegerDigits[Prime[++n]], 1]) != {}, Sow[a[[1, 1]]]]][[2, 1]]] (* Paolo Xausa, Aug 01 2024 *)

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

Extensions

Edited by Klaus Brockhaus, Feb 15 2007