cp's OEIS Frontend

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

%I A069677 #31 Aug 28 2021 03:16:20
%S A069677 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,
%T A069677 97,127,223,227,229,421,521,523,727,821,823,827,829,929,1223,1229,
%U A069677 2221,3221,3229,4229,5227,6221,6229,7229,8221,9221,9227,12227,22229,42221
%N A069677 Primes with either no internal digits or all internal digits are 2.
%H A069677 Michael S. Branicky, <a href="/A069677/b069677.txt">Table of n, a(n) for n = 1..275</a> (1..80 from Harvey P. Dale, 81..178 from David A. Corneth, all terms with <= 1000 digits)
%t A069677 Join[Prime[Range[25]],Select[Prime[Range[26,4500]],Union[Most[ Rest[ IntegerDigits[ #]]]] =={2}&]] (* _Harvey P. Dale_, Aug 12 2021 *)
%o A069677 (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
%o A069677 (Python)
%o A069677 from sympy import isprime
%o A069677 def agen(maxdigits):
%o A069677     yield from [2, 3, 5, 7]
%o A069677     for d in range(2, maxdigits+1):
%o A069677         pow10, mid = 10**(d-1), 0 if d < 3 else 10*int('2'*(d-2))
%o A069677         cands = (a*pow10+mid+b for a in range(1, 10) for b in [1, 3, 7, 9])
%o A069677         yield from filter(isprime, cands)
%o A069677 print([an for an in agen(100)]) # _Michael S. Branicky_, Aug 12 2021
%Y A069677 Cf. A069675, A069676, A069678, A069679, A069680, A069681, A069682, A069683, A069684.
%K A069677 nonn,base
%O A069677 1,1
%A A069677 _Amarnath Murthy_, Apr 06 2002
%E A069677 Corrected by _Ray Chandler_, Nov 24 2003
%E A069677 Offset corrected and name changed by _Arkadiusz Wesolowski_, Sep 07 2011