A119378 Palindromic composites such that some digit permutation is prime.

121, 232, 272, 292, 323, 343, 434, 494, 575, 616, 737, 767, 818, 838, 878, 949, 959, 979, 10201, 10801, 10901, 11011, 11611, 11711, 11911, 12121, 12221, 12521, 13031, 13231, 13531, 13631, 14041, 14141, 14641, 14941, 15151, 15251, 15751, 15851, 16261, 16861, 16961

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

121 is composite that have a prime digit permutation: 211.
1001 is composite, but is not a term since 0011, though prime, contains leading zeros, which is not allowed here.

Mathematica

palQ[n_Integer, base_Integer] := Module[{idn = IntegerDigits[n, base]}, idn == Reverse@idn]; fQ[n_] := Union[PrimeQ /@ FromDigits /@ Permutations@ IntegerDigits@n][[ -1]] == True; Select[Range@15850, !PrimeQ@# && palQ[ #, 10] && fQ@# &] (* Robert G. Wilson v,  Aug 04 2006 *)

Prog

(Python)
from sympy import isprime
from itertools import count, islice, product
from sympy.utilities.iterables import multiset_permutations as mp
def pals(base=10): # generator for all palindromes as strings
  digits = "".join(str(i) for i in range(base))
  for d in count(1):
    for p in product(digits, repeat=d//2):
        if d//2 > 0 and p[0] == "0": continue
        left = "".join(p); right = left[::-1]
        for mid in [[""], digits][d%2]: yield left + mid + right
def ok(s): # where s is string of digits
    if isprime(int(s)): return False
    return any(p[0]!="0" and isprime(int("".join(p))) for p in mp(s))
def agen():
    yield from (int(s) for s in pals() if ok(s))
print(list(islice(agen(), 43))) # Michael S. Branicky, Nov 27 2022

Crossrefs

Sequence in context: A275028 A036309 A346507 * A261618 A084998 A082944

Adjacent sequences: A119375 A119376 A119377 * A119379 A119380 A119381

Keyword

base,nonn

Author

Tanya Khovanova, Jul 24 2006

Extensions

More terms from Joshua Zucker and Robert G. Wilson v, Aug 04 2006

a(41) and beyond from Michael S. Branicky, Nov 27 2022

Status

approved