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A229075 Primes of the form p^2 + q^2 + 21, where p and q are consecutive primes. 1

%I

%S 191,311,479,911,1823,2351,4079,5039,6311,8231,9551,10391,13151,14831,

%T 17351,22079,24671,33311,35951,41543,51239,57839,61991,69263,73751,

%U 76079,84143,101279,103991,106751,111431,115223,141551,145823,198479,210071,223151,263591

%N Primes of the form p^2 + q^2 + 21, where p and q are consecutive primes.

%C Conjecture: the expression p^2+q^2+c with p and q consecutive primes and c=21 generates more primes than any other value of c in the range 1..150. Hence, c=21 is considered for this sequence.

%H K. D. Bajpai, <a href="/A229075/b229075.txt">Table of n, a(n) for n = 1..5000</a>

%e a(1) = 191: prime(4)^2 + prime(4+1)^2 + 21 = 191, which is prime.

%p KD:= proc() local a; a:= ithprime(n)^2+ithprime(n+1)^2+21; if isprime(a) then RETURN(a): fi; end: seq(KD(),n=1..300);

%t Select[Table[Prime[n]^2 + Prime[n + 1]^2 + 21, {n, 100}], PrimeQ] (* _T. D. Noe_, Sep 12 2013 *)

%Y Cf. A072669, A227340.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Sep 12 2013

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Last modified May 25 20:09 EDT 2022. Contains 354071 sequences. (Running on oeis4.)