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

%I A037024 #21 Aug 01 2024 08:04:17
%S A037024 6,9,4,13,94,110,95,37,16,186,137,46,2,23,119,8,4,219,98,39,299,13,26,
%T A037024 11,12,852,3486,1487,206,362,297,1096,859,525,2606,393,1657,1410,1182,
%U A037024 428,438,728,1944,168,37,704,93,135,484,185,229,1688,1707,1713,1006
%N A037024 Position of start of first occurrence of prime(n) after the decimal point in expansion of Pi.
%H A037024 Michael S. Branicky, <a href="/A037024/b037024.txt">Table of n, a(n) for n = 1..10000</a>
%H A037024 Dave Andersen, <a href="http://www.angio.net/pi/piquery">The Pi-Search Page</a>
%e A037024 Pi = 3.14159265358979323846264338327950288... (see A000796).
%e A037024 First occurrence of prime(23) = 83 starts at the 26th digit after the decimal point, hence a(23) = 26.
%t A037024 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 *)
%o A037024 (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 */
%o A037024 (Python)
%o A037024 from itertools import takewhile
%o A037024 from sympy import S, prime, primerange
%o A037024 # download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
%o A037024 # with open('pi-billion.txt', 'r') as f: pi_digits = f.readline()[1:]
%o A037024 pi_digits = str(S.Pi.n(10**4))[1:] # alternative to above
%o A037024 def aupton(nn):
%o A037024     plocs = (pi_digits.find(str(p)) for p in primerange(2, prime(nn)+1))
%o A037024     return list(takewhile(lambda x: x>=0, plocs)) # until p not found
%o A037024 print(aupton(55)) # _Michael S. Branicky_, Jun 12 2021
%Y A037024 Cf. A000796, A014777.
%K A037024 nonn,base
%O A037024 1,1
%A A037024 _Patrick De Geest_, Jan 04 1999
%E A037024 Edited by _Klaus Brockhaus_, Feb 15 2007