A198344 -id:A198344 - cp's OEIS frontend

A104842 Position of the first sequence of n subsequent digits of Pi which form a prime.

1, 1, 8, 3, 2, 1, 4, 34, 30, 5, 15, 2, 6, 17, 36, 82, 12, 87, 26, 12, 25, 133, 35, 18, 17, 3, 41, 17, 234, 17, 167, 92, 251, 15, 9, 12, 31, 1, 57, 290, 4, 99, 98, 502, 48, 164, 198, 201, 128, 7, 363, 143, 11, 138, 196, 32, 230, 82, 292, 515, 334, 186, 176, 223, 57, 135, 35

Offset: 1

Zak Seidov, Mar 27 2005

Note that values with indices n = 22, 43, 55, ... are positions of primes with leading zeros, which is in particular manifest from a(42)=99, a(43)=98. See A198344 for the position of the "true" n-digit primes listed in A104841. - M. F. Hasler, Oct 23 2011

			a(1)=1 since the first single-digit prime found, 3, is at first place, hence a(1)=1,
a(2)=1 since the first two-digit prime found, 31, is at first place, hence a(2)=1,
a(3)=8 since the first three-digit prime found, 653, is at 8th place, hence a(3)=8, ...

Cf. A104819 - A104841, A198344.

pi = RealDigits[Pi, 10, 100][[1]]; f[n_] := Block[{k = 1}, While[ !PrimeQ[ FromDigits[ Take[pi, {k, k + n - 1}]]], k++ ]; k]; Table[ f[n], {n, 67}] (* Robert G. Wilson v, Mar 29 2005 *)

a(n)={for(c=-1,default(realprecision)-n-2,ispseudoprime(Pi\.1^(n+c)%10^n)&return(c+2));error("Insufficient realprecision, please increase.")}  \\  M. F. Hasler, Oct 23 2011

More terms from a(33) onward from Robert G. Wilson v, Mar 29 2005

A104841 The first n-digit prime occurring in the decimal expansion of Pi, A000796.

Original entry on oeis.org

3, 31, 653, 4159, 14159, 314159, 1592653, 28841971, 795028841, 5926535897, 93238462643, 141592653589, 9265358979323, 23846264338327, 841971693993751, 8628034825342117, 89793238462643383, 348253421170679821, 3832795028841971693, 89793238462643383279

Offset: 1

Zak Seidov, Mar 27 2005

For the next n-digit primes, see the b-file (link).

Sequence A198344 gives the position of these primes withing the digits of Pi.

Michael S. Branicky, Table of n, a(n) for n = 1..1000 (terms 1..162 from M. F. Hasler)

Cf. A104819 - A104842.

Cf. A000796, A198344.

default(realprecision,2000); A104841(n)={for( c=0, default(realprecision)-n-2, Pi\.1^c%10 & ispseudoprime(p=Pi\.1^(n+c-1)%10^n) & return(p));error("Please increase default(realprecision) to calculate A104841("n").")}  \\ M. F. Hasler, Oct 23 2011

from sympy import S, isprime
pi = "3"+str(S.Pi.n(10**5))[2:] # or load data from file
def A104841_A198344(n): return next(((p, i+1) for i in range(len(pi)-n) if pi[i]!="0" and isprime(p:=int(pi[i:i+n]))), "not enough digits")
print([A104841_A198344(n)[0] for n in range(1, 21)]) # Michael S. Branicky, Dec 28 2022

A272304 Position of the first n-digit prime occurring in the decimal expansion of e.

Original entry on oeis.org

1, 2, 1, 15, 25, 13, 1, 65, 20, 100, 38, 54, 8, 48, 40, 41, 9, 83, 152, 19, 52, 6, 16, 66, 4, 4, 69, 25, 28, 7, 97, 174, 4, 48, 127, 11, 40, 58, 48, 69, 45, 40, 34, 119, 6, 7, 92, 61, 2, 40, 138, 105, 332, 28, 70, 322, 62, 231, 78, 339, 245, 66, 49, 439, 298

Offset: 1

Harvey P. Dale, Apr 25 2016

Leading zeros are not allowed.

			a(1) = 1 because the initial digit "2" of e is prime.

Harvey P. Dale, Table of n, a(n) for n = 1..200

Cf. A001113, A198344.

With[{ed = RealDigits[E, 10, 10000][[1]]}, Table[Position[Partition[ed, n, 1], _?(PrimeQ[FromDigits[#]] && #[[1]] != 0 &), {1}, 1, Heads -> False], {n, 100}]] // Flatten

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A104842 Position of the first sequence of n subsequent digits of Pi which form a prime.

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A104841 The first n-digit prime occurring in the decimal expansion of Pi, A000796.

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Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Python

A272304 Position of the first n-digit prime occurring in the decimal expansion of e.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica