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A245571 a(n) is the smallest prime number with at least two digits formed by the concatenation of the subsequent digits of Pi, starting at the n-th digit, ignoring the decimal point. 1
31, 14159, 41, 1592653, 59, 9265358979323, 26535897932384626433832795028841971693993751058209, 653, 53, 35897, 5897, 89, 97, 79, 9323, 32384626433832795028841971693993751058209749445923078164062862089986280348253421, 23, 38462643383 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(19) has 3057 digits. - Robert Israel, Aug 27 2014

a(20) = 462643. - Felix Fröhlich, Aug 30 2014

a(21) has >= 3490 digits, a(22) = 2643383, a(22)-a(42) have 20 or fewer digits. - Chai Wah Wu, Sep 24 2014

LINKS

Table of n, a(n) for n=1..18.

EXAMPLE

a(4) = 1592653, because starting at the 4th digit in the expansion, the smallest substring of the digits of Pi forming a prime number is 3.14|1592653|589...

MAPLE

N:= 1000: # to use up to N+1 digits of pi.

nmax:= 30: # to get up to a(nmax), if possible.

S:= floor(10^N*Pi):

L:= ListTools:-Reverse(convert(S, base, 10)):

for n from 1 to nmax do

  p:= L[n];

  for k1 from n+1 to N+1 do

    p:= 10*p + L[k1];

    if isprime(p) then break fi

  od:

  if k1 > N+1 then

    A[n]:= "Ran out of digits";

    break

   else

    A[n]:= p

  end

od:

seq(A[i], i=1..n-1); # Robert Israel, Aug 27 2014

PROG

(Python)

from sympy.mpmath import *

from sympy import isprime

def A245571(n):

....mp.dps = 1000+n

....s = nstr(pi, mp.dps)[:-1].replace('.', '')[n-1:]

....for i in range(len(s)-1):

........p = int(s[:i+2])

........if p > 10 and isprime(p):

............return p

....else:

........return 'Ran out of digits'

# Chai Wah Wu, Sep 16 2014, corrected Chai Wah Wu, Sep 24 2014

CROSSREFS

Cf. A000796, A005042, A047777, A076094, A104841, A195834, A198018, A198019, A198187.

Sequence in context: A261947 A069451 A073099 * A074218 A161395 A215610

Adjacent sequences:  A245568 A245569 A245570 * A245572 A245573 A245574

KEYWORD

nonn,base

AUTHOR

Felix Fröhlich, Aug 22 2014

STATUS

approved

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Last modified September 16 23:53 EDT 2021. Contains 347477 sequences. (Running on oeis4.)