A111382 Beginning with 3, least number such that concatenation of first n terms and its digit reversal both are primes.

3, 1, 1, 21, 11, 43, 47, 157, 753, 51, 917, 273, 2409, 703, 413, 3729, 1153, 6243, 8789, 2307, 4477, 137, 403, 10649, 4617, 4533, 6133, 4721, 877, 2469, 5967, 1557, 1047, 38931, 15533, 6877, 23987, 4767, 18049, 1463, 118333, 27897

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..160

Maple

rev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc;
R:= 3: X:= 3: XR:= 3:
for i from 2 to 50 do
  for x from 1 by 2 do
    d:= 1+ilog10(x);
    t:= X*10^(1+ilog10(x)) + x;
    if not isprime(t) then next fi;
    xr:= rev(x);
    tr:= XR+xr*10^(1+ilog10(XR));
    if isprime(tr) then break fi;
  od;
  X:= t; XR:= tr; R:= R, x;
od:
R; # Robert Israel, Aug 09 2023

Prog

(Python)
from itertools import count, islice
from gmpy2 import digits, is_prime, mpz
def agen(): # generator of terms
    s, r, an = "", "", 3
    while True:
        yield int(an)
        d = digits(an)
        s, r, k, sk = s+d, d[::-1]+r, 1, "1"
        while not is_prime(mpz(s+sk)) or not is_prime(mpz(sk[::-1]+r)):
            k += 2
            if k%10 == 5: k += 2
            sk = digits(k)
        an = k
print(list(islice(agen(), 42))) # Michael S. Branicky, Jan 02 2025

Crossrefs

Cf. A113584.

Sequence in context: A121412 A212855 A016561 * A173884 A176418 A156950

Adjacent sequences: A111379 A111380 A111381 * A111383 A111384 A111385

Keyword

nonn,base

Author

Hans Havermann, Nov 08 2005

Status

approved