A245571 - OEIS

%I #78 Nov 02 2019 03:31:22

%S 31,14159,41,1592653,59,9265358979323,

%T 26535897932384626433832795028841971693993751058209,653,53,35897,5897,

%U 89,97,79,9323,32384626433832795028841971693993751058209749445923078164062862089986280348253421,23,38462643383

%N 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.

%C a(19) has 3057 digits. - _Robert Israel_, Aug 27 2014

%C a(20) = 462643. - _Felix Fröhlich_, Aug 30 2014

%C a(21) has >= 3490 digits, a(22) = 2643383, a(22)-a(42) have 20 or fewer digits. - _Chai Wah Wu_, Sep 24 2014

%e 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...

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

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

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

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

%p for n from 1 to nmax do

%p   p:= L[n];

%p   for k1 from n+1 to N+1 do

%p     p:= 10*p + L[k1];

%p     if isprime(p) then break fi

%p   od:

%p   if k1 > N+1 then

%p     A[n]:= "Ran out of digits";

%p     break

%p    else

%p     A[n]:= p

%p   end

%p od:

%p seq(A[i],i=1..n-1); # _Robert Israel_, Aug 27 2014

%o (Python)

%o from sympy.mpmath import *

%o from sympy import isprime

%o def A245571(n):

%o ....mp.dps = 1000+n

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

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

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

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

%o ............return p

%o ....else:

%o ........return 'Ran out of digits'

%o # _Chai Wah Wu_, Sep 16 2014, corrected _Chai Wah Wu_, Sep 24 2014

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

%K nonn,base

%O 1,1

%A _Felix Fröhlich_, Aug 22 2014