A056732 -id:A056732 - cp's OEIS frontend

A028989 Smallest palindromic prime with 2n-1 digits.

2, 101, 10301, 1003001, 100030001, 10000500001, 1000008000001, 100000323000001, 10000000500000001, 1000000008000000001, 100000000212000000001, 10000000000300000000001, 1000000000016100000000001, 100000000000080000000000001, 10000000000000300000000000001

Offset: 1

Patrick De Geest

Charles R Greathouse IV, Table of n, a(n) for n = 1..500
Patrick De Geest, World!Of Palindromic Primes.

Odd-numbered terms of A056732. - Edward Catmur, May 01 2015

Cf. A100027.

t={}; Do[p=NextPrime[10^(2*n)]; While[Reverse[x=IntegerDigits[p]]!=x,p=NextPrime[p]]; AppendTo[t,p],{n,0,6}]; t (* Jayanta Basu, Jun 05 2013 *)

a(n)={
n--;
my(N=100^n+1,aS=10^(n+3)+10^(n-3),bS=10^(n+2)+10^(n-2),cS=10^(n+1)+10^(n-1),dS=10^n);
forstep(a=N,N+9*aS,aS,
forstep(b=a,a+9*bS,bS,
forstep(c=b,b+9*cS,cS,
forstep(d=c,c+9*dS,dS,
if(ispseudoprime(d),return(d))
))));
warning("could not find a("n")")
}; \\ Charles R Greathouse IV, Feb 15 2011

a(n)=for(j=10^(n-1),10^n-1,d=digits(j);p=fromdigits(vector(2*n-1,x,if(xJeppe Stig Nielsen, Feb 20 2021

a(10) corrected by Farideh Firoozbakht, Oct 10 2005

A115941 a(n) is the least prime whose representation contains a palindromic substring of length n.

Original entry on oeis.org

2, 11, 101, 11113, 10301, 1011013, 1003001, 100110013, 100030001, 10000000019, 10000500001, 1000011000017, 1000008000001, 100000440000011, 100000323000001, 10000001100000011, 10000000500000001, 1000000011000000019, 1000000008000000001, 100000000660000000013

Offset: 1

Giovanni Resta, Feb 06 2006

			a(6)=1011013 since it is the least prime that contains a palindromic substring (101101) of length 6.

Michael S. Branicky, Table of n, a(n) for n = 1..25

Cf. A056732.

from sympy import isprime
from itertools import product
def pals_to_test(n, odd=True):
  if n <= 2: yield [2, 11][n-1]
  if odd: ruled_out = "024568" # can't be even or multiple of 5
  else: ruled_out = "0"
  midrange = [[""], [str(i) for i in range(10)]]
  for p in product("0123456789", repeat=n//2):
    left = "".join(p)
    if len(left):
      if left[0] in ruled_out: continue
    for middle in midrange[n%2]:
        out = left+middle+left[::-1]
        if odd: yield out
        else:
          for last in "1379": yield out+last
def a(n):
  palsgen = pals_to_test(n, n%2 == 1)
  while True:
    strpal = next(palsgen)
    pal = int(strpal)
    if isprime(pal): return pal
print([a(n) for n in range(1, 18)]) # Michael S. Branicky, Feb 11 2021

a(18) and beyond from Michael S. Branicky, Feb 11 2021

cp's OEIS Frontend

A028989 Smallest palindromic prime with 2n-1 digits.

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