A382927 Smallest beginning of a sequence of exactly n consecutive palindromic primes, all ending with the same digit.

2, 181, 151, 131, 101, 11, 17471, 16661, 16561, 16361, 16061, 15551, 15451, 14741, 14341, 13931, 13831, 13331, 12821, 12721, 12421, 11411, 11311, 10601, 10501, 10301, 1884881, 1883881, 1881881, 1880881, 1879781, 1878781, 1876781, 1865681, 1856581, 1853581, 1851581

Offset: 1

Author

Jean-Marc Rebert, Apr 13 2025

Keywords

• nonn
• base

Examples

			a(6) = 11, because 11 initiates a sequence of exactly six consecutive palindromic primes: 11, 101, 131, 151, 181 and 191, each ending in the same digit 1.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002385, A054681.

Programs

Maple

# with A002385 e.g. from the b-file for that sequence
R:= NULL:
d:= 2: count:= 1: m:= 1;
for i from 2 while m < 100 do
  dp:= A002385[i] mod 10;
  if d = dp then count:= count+1
  else
    d:= dp;
    if count >= m then
      R:= R, seq(A002385[i-j],j=m..count);
      m:= count+1;
    fi;
    count:= 1;
  fi
od:
R; # Robert Israel, May 13 2025

Python

from sympy import isprime
from itertools import count, islice, product
def palprimes(): # generator of palprimes
    yield from [2, 3, 5, 7, 11]
    for d in count(3, 2):
        for last in "1379":
            for p in product("0123456789", repeat=d//2-1):
                left = "".join(p)
                for mid in [[""], "0123456789"][d&1]:
                    t = int(last + left + mid + left[::-1] + last)
                    if isprime(t):
                        yield t
def agen(): # generator of terms
    adict, n, lastdigit, vlst = dict(), 1, 0, [2]
    for p in palprimes():
        if p%10 == lastdigit:
            vlst.append(p)
        else:
            if len(vlst) >= n:
                for i in range(n, len(vlst)+1):
                    if i not in adict:
                        adict[i] = vlst[-i]
                while n in adict: yield adict[n]; n += 1
            lastdigit, vlst = p%10, [p]
print(list(islice(agen(), 40))) # Michael S. Branicky, Apr 13 2025