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%I #16 Nov 18 2023 07:26:50
%S 2,3,9,11,313,33,9339,303,909,747,383,7,969,797,141,12721,1881,161,
%T 343,77,333,7227,181,737,30603,14841,12621,1111,15051,777,939,7887,
%U 7997,13231,191,79297,13331,11511,19191,38583,3993,949,17171,15351,318813
%N a(1) = 2; then smallest palindrome > 1 not occurring earlier such that every partial concatenation is a prime.
%H Robert Israel, <a href="/A088086/b088086.txt">Table of n, a(n) for n = 1..635</a>
%e 2, 23, 239, 23911, etc. are primes.
%p A:= [1,3,7,9]: B:= [1,3,7,9]:
%p P:= 3,7,9,op(zip((s,t) -> s*10+t, A, B)):
%p for d from 1 to 6 do
%p 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)):
%p A:= map(proc(t) local i; seq(10*t+i,i=0..9) end proc, A);
%p B:= map(proc(t) local i; seq(10^d*i+t, i=0..9) end proc, B);
%p P:= P, op(zip((s,t) -> 10^(d+1)*s+t,A,B));
%p od:
%p P:= [P]:
%p R:= 2: p:= 2:
%p for i from 2 to 50 do
%p for j from 1 do
%p v:= p*10^(1+ilog10(P[j]))+P[j];
%p if isprime(v) then
%p p:= v;
%p R:= R, P[j];
%p P:= subsop(j=NULL, P);
%p break
%p fi
%p od od:
%p R; # _Robert Israel_, Nov 15 2023
%o (Python)
%o from gmpy2 import is_prime
%o from itertools import count, islice, product
%o def bgen(): # generator of palindromic decimal strings ending in 1, 3, 7, 9
%o yield from "379"
%o for digits in count(2):
%o for first in "1379":
%o for left in product("0123456789", repeat=(digits-2)//2):
%o left = "".join(left)
%o right = left[::-1]
%o for mid in [[""], "0123456789"][digits%2]:
%o yield first + left + mid + right + first
%o def agen():
%o alst, aset, concat = [2], {"2"}, "2"
%o while True:
%o yield alst[-1]
%o g = bgen()
%o s = next(g)
%o while "start" in s or s in aset or not is_prime(int(concat + s)):
%o s = next(g)
%o concat += s
%o aset.add(s)
%o alst.append(int(s))
%o print(list(islice(agen(), 45))) # _Michael S. Branicky_, Nov 18 2023
%Y Cf. A088087, A088084.
%K base,nonn
%O 1,1
%A _Amarnath Murthy_, Sep 22 2003
%E More terms from _Sam Alexander_, Nov 17 2003
%E More terms from _David Wasserman_, Jul 13 2005
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