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

1,1

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)

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A069676 A062353 A077390 * A069678 A069679 A069680

Adjacent sequences: A069674 A069675 A069676 * A069678 A069679 A069680

Keyword

nonn,base

Author

Amarnath Murthy, Apr 06 2002

Extensions

Corrected by Ray Chandler, Nov 24 2003

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

Status

approved