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.

31, 14159, 41, 1592653, 59, 9265358979323, 26535897932384626433832795028841971693993751058209, 653, 53, 35897, 5897, 89, 97, 79, 9323, 32384626433832795028841971693993751058209749445923078164062862089986280348253421, 23, 38462643383

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: A069451 A374668 A073099 * A074218 A161395 A215610

Adjacent sequences: A245568 A245569 A245570 * A245572 A245573 A245574

Keyword

nonn,base

Author

Felix Fröhlich, Aug 22 2014

Status

approved