1,1

Note that all terms after the first two are equal to 11 modulo 72 and that (a(n)-11)/72 is a triangular number, since they have to be 2 more than the square of an odd multiple of 3 to be prime and if k=6m+3 then a(n)=k^2+2=72m(m+1)/2+11.

The quotient cycle length is 2 in the continued fraction expansion of sqrt(p) for these primes. E.g.: cfrac(sqrt(6563),6)= 81+1/(81+1/(162+1/(81+1/(162+1/(81+1/(162+`...`)))))) - Labos E. (labos(AT)ana.sote.hu), Feb 22 2001

Primes in A059100; except for a(2)=3 a subsequence of A007491 and congruent to 2 modulo 9. For n>2, a(n)=11 (mod 72). [From M. F. Hasler (MHasler(AT)univ-ag.fr), Apr 05 2009]

M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988

Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997

Eric Weisstein's World of Mathematics, Near-Square Prime

For n>1, a(n)=72*A000217(A056900(n-2))+11

Also, primes of form n^2 - 2n + 3.

a(n)=A067201(n)^2+2. [From M. F. Hasler (MHasler(AT)univ-ag.fr), Apr 05 2009]

Intersection[Table[n^2+2, {n, 0, 10^2}], Prime[Range[9*10^3]]] ...or... For[i=2, i<=2, a={}; Do[If[PrimeQ[n^2+i], AppendTo[a, n^2+i]], {n, 0, 100}]; Print["n^2+", i, ", ", a]; i++ ] - Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 29 2008

Cf. A002496.

Sequence in context: A008510 A042165 A089921 this_sequence A117699 A065378 A161721

Adjacent sequences: A056896 A056897 A056898 this_sequence A056900 A056901 A056902

nonn

Henry Bottomley (se16(AT)btinternet.com), Jul 05 2000