A354510 - OEIS

%I #15 Aug 18 2022 11:45:01

%S 13007,28211,36857,39227,86441,272507,345731,459671,467867,553529,

%T 599087,746507,777911,788561,910127,1354901,1425653,1512923,1587587,

%U 1710869,2039171,2509061,2624411,3196913,3617597,3896657,4161611,4260077,4359749,4460549,4536893,4639757,5171093,5280791,5673911,5963351

%N Primes of the form p+q^2+r where p,q,r are three consecutive members of A007528.

%C Primes of the form p+q^2+r where p, q and r are consecutive members of the sequence of primes of the form 6*k-1.

%C All terms == 5 (mod 6).

%H Robert Israel, <a href="/A354510/b354510.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 36857 is in the sequence because 36857 = 179 + 191^2 + 197 and 179 = A007528(21), 191 = A007528(22) and 197 = A007528(23).

%p q:= 5: r:= 11: count:= 0: R:= NULL:

%p while count < 40 do

%p   p:= q; q:= r;

%p   do r:= r+6 until isprime(r);

%p   if isprime(p+q^2+r) then count:= count+1; R:= R, p+q^2+r fi

%p od:

%p R;

%t Select[#[[1]] + #[[2]]^2 + #[[3]] & /@ Partition[Select[Prime[Range[400]], Mod[#1, 6] == 5 &], 3, 1], PrimeQ] (* _Amiram Eldar_, Aug 16 2022 *)

%Y Cf. A007528.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Aug 16 2022