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

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

Offset

1,1

Links

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

Example

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

Prog

(Python)
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

Crossrefs

Cf. A056732.

Sequence in context: A089393 A069664 A130150 * A351622 A024721 A367852

Adjacent sequences: A115938 A115939 A115940 * A115942 A115943 A115944

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

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

Status

approved