A088086 a(1) = 2; then smallest palindrome > 1 not occurring earlier such that every partial concatenation is a prime.

2, 3, 9, 11, 313, 33, 9339, 303, 909, 747, 383, 7, 969, 797, 141, 12721, 1881, 161, 343, 77, 333, 7227, 181, 737, 30603, 14841, 12621, 1111, 15051, 777, 939, 7887, 7997, 13231, 191, 79297, 13331, 11511, 19191, 38583, 3993, 949, 17171, 15351, 318813

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..635

Example

2, 23, 239, 23911, etc. are primes.

Maple

A:= [1, 3, 7, 9]: B:= [1, 3, 7, 9]:
P:= 3, 7, 9, op(zip((s, t) -> s*10+t, A, B)):
for d from 1 to 6 do
  P:= P, op(zip(proc(s, t) local i; seq(10^(d+1)*s + 10^d*i + t, i=0..9) end proc, A, B)):
  A:= map(proc(t) local i; seq(10*t+i, i=0..9) end proc, A);
  B:= map(proc(t) local i; seq(10^d*i+t, i=0..9) end proc, B);
  P:= P, op(zip((s, t) -> 10^(d+1)*s+t, A, B));
od:
P:= [P]:
R:= 2: p:= 2:
for i from 2 to 50 do
  for j from 1 do
    v:= p*10^(1+ilog10(P[j]))+P[j];
    if isprime(v) then
      p:= v;
      R:= R, P[j];
      P:= subsop(j=NULL, P);
      break
    fi
od od:
R; # Robert Israel, Nov 15 2023

Prog

(Python)
from gmpy2 import is_prime
from itertools import count, islice, product
def bgen(): # generator of palindromic decimal strings ending in 1, 3, 7, 9
    yield from "379"
    for digits in count(2):
        for first in "1379":
            for left in product("0123456789", repeat=(digits-2)//2):
                left = "".join(left)
                right = left[::-1]
                for mid in [[""], "0123456789"][digits%2]:
                    yield first + left + mid + right + first
def agen():
    alst, aset, concat = [2], {"2"}, "2"
    while True:
        yield alst[-1]
        g = bgen()
        s = next(g)
        while "start" in s or s in aset or not is_prime(int(concat + s)):
            s = next(g)
        concat += s
        aset.add(s)
        alst.append(int(s))
print(list(islice(agen(), 45))) # Michael S. Branicky, Nov 18 2023

Crossrefs

Cf. A088087, A088084.

Sequence in context: A287680 A242680 A275767 * A088084 A182203 A168080

Adjacent sequences: A088083 A088084 A088085 * A088087 A088088 A088089

Keyword

base,nonn

Author

Amarnath Murthy, Sep 22 2003

Extensions

More terms from Sam Alexander, Nov 17 2003

More terms from David Wasserman, Jul 13 2005

Status

approved