1,1

a(n) mod 24 = 5 or 13 and if a(n) mod 24 =13 then a(n) mod 72 = 13.

For n>=2 a(n)= A098062(n-1). - Zak Seidov, Apr 12 2007

Contribution from Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008: (Start)

Primes p such that continued fraction of (1+Sqrt[p])/2 has period 1.

Primes in A078370 = primes of the form 4 k^2 + 4 k + 5. (End)

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

D. Shanks, The simplest cubic fields, Math. Comp., 28 (1974), 1137-1152.

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

a(n)=24*A056904(n)+m, where m=13 if A056904(n) is three times a triangular number (and n>0) and m=5 if A056904(n) is not three times a triangular number (or n=0).

a(2)=29 since 29=5^2+4 is prime.

Intersection[Table[n^2+4, {n, 0, 10^2}], Prime[Range[9*10^3]]] ...or... For[i=4, i<=4, 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

aa = {}; Do[If[PrimeQ[4 k^2 + 4 k + 5], AppendTo[aa, 4 k^2 + 4 k + 5]], {k, 0, 200}]; aa [From Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008]

a(n)-4 is contained in A016754. (a(n)-5)/8 is contained in A000217. Either (a(n)-5)/24 is contained in A001318 (if a(n) mod 24=5) or (a(n)-13)/72 is contained in A000217 (if a(n) mod 24=13). Floor[a(n)/24] is contained in A001840.

A146326 [From Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008]

Sequence in context: A130230 A106931 A078370 this_sequence A086732 A162329 A160430

Adjacent sequences: A005470 A005471 A005472 this_sequence A005474 A005475 A005476

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms and additional comments from Henry Bottomley (se16(AT)btinternet.com), Jul 06 2000