A069677 Primes with either no internal digits or all internal digits are 2.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 127, 223, 227, 229, 421, 521, 523, 727, 821, 823, 827, 829, 929, 1223, 1229, 2221, 3221, 3229, 4229, 5227, 6221, 6229, 7229, 8221, 9221, 9227, 12227, 22229, 42221

Offset: 1

Author

Amarnath Murthy, Apr 06 2002

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..275 (1..80 from Harvey P. Dale, 81..178 from David A. Corneth, all terms with <= 1000 digits)

Crossrefs

Cf. A069675, A069676, A069678, A069679, A069680, A069681, A069682, A069683, A069684.

Programs

Mathematica

Join[Prime[Range[25]],Select[Prime[Range[26,4500]],Union[Most[ Rest[ IntegerDigits[ #]]]] =={2}&]] (* Harvey P. Dale, Aug 12 2021 *)

PARI

uptoqdigits(n) = { my(ld = [1,3,7,9]); n = max(n, 2); res = List(primes(primepi(97))); for(i = 1, n-2, twos = 20*(10^i\9); for(j = 1, 9, for(k = 1, #ld, c = j*10^(i+1) + twos + ld[k]; if(isprime(c), listput(res, c) ) ) ) ); Set(res) } \\ David A. Corneth, Aug 12 2021

Python

from sympy import isprime
def agen(maxdigits):
    yield from [2, 3, 5, 7]
    for d in range(2, maxdigits+1):
        pow10, mid = 10**(d-1), 0 if d < 3 else 10*int('2'*(d-2))
        cands = (a*pow10+mid+b for a in range(1, 10) for b in [1, 3, 7, 9])
        yield from filter(isprime, cands)
print([an for an in agen(100)]) # Michael S. Branicky, Aug 12 2021

Extensions

Corrected by Ray Chandler, Nov 24 2003

Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011