A105127 -id:A105127 - cp's OEIS frontend

A105126 Primes of the form 16n+9.

41, 73, 89, 137, 233, 281, 313, 409, 457, 521, 569, 601, 617, 761, 809, 857, 937, 953, 1033, 1049, 1097, 1129, 1193, 1289, 1321, 1433, 1481, 1609, 1657, 1721, 1753, 1801, 1913, 1993, 2089, 2137, 2153, 2281, 2297, 2377, 2393, 2441, 2473, 2521, 2617, 2633, 2713

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

nonn

A prime of the form 16n+9 is represented by exactly one of x^2 + 32y^2 and x^2 + 64y^2 (see Kaplanski link). - Michel Marcus, Dec 23 2012

T. D. Noe, Table of n, a(n) for n = 1..1000
Irving Kaplansky, The forms x+32y^2 and x+64y^2, Proc. Amer. Math. Soc. 131 (2003), 2299-2300

Cf. A002145, A007521, A105127-A105132.

M:=500; f:=proc(n) local t1,t2; t1:=[]; for k from 0 to M do t2:=2^n*k+2^(n-1)+1; if isprime(t2) then t1:=[op(t1),t2]; fi; od; t1; end; f(4);

lst={};Do[p=16*n+9;If[PrimeQ[p],AppendTo[lst,p]],{n,0,3*5!,1}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 27 2009 *)

select(n->n%16==9, primes(500)) \\ Charles R Greathouse IV, Apr 29 2015

A339900 Lexicographically earliest permutation of odd primes such that A007814(a(n)-1) = 1+A007814(n), where A007814 gives the 2-adic valuation of n.

Original entry on oeis.org

3, 5, 7, 41, 11, 13, 19, 17, 23, 29, 31, 73, 43, 37, 47, 97, 59, 53, 67, 89, 71, 61, 79, 113, 83, 101, 103, 137, 107, 109, 127, 193, 131, 149, 139, 233, 151, 157, 163, 241, 167, 173, 179, 281, 191, 181, 199, 353, 211, 197, 223, 313, 227, 229, 239, 337, 251, 269, 263, 409, 271, 277, 283, 641, 307, 293, 311, 457, 331

Offset: 1

Antti Karttunen, Dec 25 2020

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A001511, A007814, A065091.
Cf. A002145 (odd bisection), A007521 (quadrisection starting from 5), A105126, A105127, A105128, A105129, A105130, A105131, A105132.
Cf. also A108546, A111745.

A339900(n) = { my(lev=1+valuation(n,2), k=(1+(n>>(lev-1)))/2); forprime(p=3,,if(valuation(p-1,2)==lev, k--; if(!k, return(p)))); };

cp's OEIS Frontend

A105126 Primes of the form 16n+9.

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