cp's OEIS Frontend

A055781 Primes q of the form q = 10p + 1, where p is also prime.

%I A055781 #49 Feb 18 2019 16:22:16
%S A055781 31,71,131,191,311,431,971,1031,1091,1511,1571,1811,1931,2111,2411,
%T A055781 2711,3371,3491,3671,4091,4211,4391,4871,5231,5471,5711,6011,6131,
%U A055781 6311,6911,7331,7691,8111,8231,8291,8831,9371,10091,10211,10331,10391,10631
%N A055781 Primes q of the form q = 10p + 1, where p is also prime.
%C A055781 Corresponding values of p in A023237. - _Jaroslav Krizek_, Jul 14 2010
%C A055781 From _Sergey Pavlov_, Jun 14 2017: (Start)
%C A055781 Let a, b, and c be prime numbers such that c = 10b + 1 = 10 * (10a + 1) + 1. Then c = 311, b = 31, a = 3. (There are no other solutions since any prime p > 3 is either of the form 3k + 1 or 3k - 1. In other words, while a > 3 and a, b are primes, a == 1 (mod 3), b == -1 (mod 3), whereas c == 0 (mod 3).)
%C A055781 So is for any similar sequence of primes (of the form kn + 1) where 2k + 1 == 0 (mod 3), e.g., for A002144: the equation of the form c = kb + 1 = k * (ka + 1) + 1 while a, b, c are primes could have the only solution iff a = 3 (but also could have not).
%C A055781 (End) [This comment needs to be rewritten. - _N. J. A. Sloane_, Feb 18 2019]
%H A055781 Robert Israel, <a href="/A055781/b055781.txt">Table of n, a(n) for n = 1..10000</a>
%e A055781 1031 = 103*10 + 1, 1 appended to 103.
%p A055781 select(isprime, map(t-> 10*t+1, select(isprime, [3,seq(i,i=7..2000,6)]))); # _Robert Israel_, Jun 13 2017
%t A055781 Select[10Prime[Range[200]]+1,PrimeQ]  (* _Harvey P. Dale_, Feb 04 2011 *)
%o A055781 (PARI) is(n)=n%10==1 && isprime(n) && isprime(n\10) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A055781 Cf. A005384, A005385, A023237.
%K A055781 nonn
%O A055781 1,1
%A A055781 _Labos Elemer_, Jul 13 2000