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

1,1

Links

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

Example

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.

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

Prog

(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

Crossrefs

Cf. A002385, A054681.

Sequence in context: A272237 A094221 A324442 * A032593 A176477 A094483

Adjacent sequences: A382924 A382925 A382926 * A382928 A382929 A382930

Keyword

nonn,base

Author

Jean-Marc Rebert, Apr 13 2025

Status

approved