A141195 -id:A141195 - cp's OEIS frontend

A094407 Primes of the form 16n+1.

17, 97, 113, 193, 241, 257, 337, 353, 401, 433, 449, 577, 593, 641, 673, 769, 881, 929, 977, 1009, 1153, 1201, 1217, 1249, 1297, 1361, 1409, 1489, 1553, 1601, 1697, 1777, 1873, 1889, 2017, 2081, 2113, 2129, 2161, 2273, 2417, 2593, 2609, 2657, 2689, 2753

Offset: 1

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jun 03 2004

Subsequence of A007519 (primes of form 8n+1). - Zak Seidov, May 16 2012
Primes p such that p XOR 14 = p + 14. - Brad Clardy, Jul 23 2012
A prime of the form 16n+1 is represented either by both x^2+32y^2 and x^2+64y^2 or by neither (see Kaplansky link). - Michel Marcus, Dec 23 2012
Odd primes p such that -1 is an 8th power mod p. - Eric M. Schmidt, Mar 27 2014

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

Primes congruent to k mod 16: A094407, A091968, A127589, A141194, A105126, A141195, A141196, A127576.

Cf. A065091, A002144, A007519, A133870, A142925, A208177, A208178, A076339.

a094407 n = a094407_list !! (n-1)
a094407_list = filter ((== 1) . a010051) [1,17..]
-- Reinhard Zumkeller, Mar 06 2012

p:=proc(n) if isprime(16*n+1)=true then 16*n+1 else fi end:seq(p(n),n=1..200); # Emeric Deutsch, Dec 23 2004

lst={};Do[p=16*n+1;If[PrimeQ[p],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)
Select[16*Range[200]+1,PrimeQ] (* Harvey P. Dale, Nov 04 2017 *)

More terms from Emeric Deutsch, Dec 23 2004

A141194 Primes of the form 16k+7.

Original entry on oeis.org

7, 23, 71, 103, 151, 167, 199, 263, 311, 359, 439, 487, 503, 599, 631, 647, 727, 743, 823, 839, 887, 919, 967, 983, 1031, 1063, 1223, 1303, 1319, 1367, 1399, 1447, 1511, 1543, 1559, 1607, 1783, 1831, 1847, 1879, 2039, 2087, 2311, 2423, 2503, 2551, 2647

Offset: 1

T. D. Noe, Jun 12 2008

nonn

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A094407, A091968, A127589, A105126, A141195, A141196, A127576.

lst={};Do[If[PrimeQ[p=16*n+7],AppendTo[lst,p]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
Select[16*Range[0,200]+7,PrimeQ] (* Harvey P. Dale, Nov 26 2015 *)

A141196 Primes of the form 16k+13.

Original entry on oeis.org

13, 29, 61, 109, 157, 173, 269, 317, 349, 397, 461, 509, 541, 557, 653, 701, 733, 797, 829, 877, 941, 1021, 1069, 1117, 1181, 1213, 1229, 1277, 1373, 1453, 1549, 1597, 1613, 1693, 1709, 1741, 1789, 1901, 1933, 1949, 1997, 2029, 2141, 2221, 2237, 2269

Offset: 1

T. D. Noe, Jun 12 2008

nonn

Which sequence, this or A141194, produces more primes? The race is very close. For example, A141194(1000)=80599 and A141196(1000)=80909, a difference of just 32 primes after a thousand terms. - Art Baker, Aug 07 2019

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A094407, A091968, A127589, A141194, A105126, A141195, A127576.

lst={};Do[If[PrimeQ[p=16*n+13],AppendTo[lst,p]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)

A228227 Primes congruent to {7, 11} mod 16.

Original entry on oeis.org

7, 11, 23, 43, 59, 71, 103, 107, 139, 151, 167, 199, 251, 263, 283, 311, 331, 347, 359, 379, 439, 443, 487, 491, 503, 523, 571, 587, 599, 619, 631, 647, 683, 727, 743, 811, 823, 827, 839, 859, 887, 907, 919, 967, 971, 983, 1019, 1031, 1051, 1063, 1163, 1223

Offset: 1

Arkadiusz Wesolowski, Aug 16 2013

nonn

Union of A141194 and A141195.

Let p be a prime number and let E(p) denote the elliptic curve y^2 = x^3 + p*x. If p is in the sequence, then the rank of E(p) is 0. Therefore A060953(a(n)) = 0.

J. H. Silverman, The arithmetic of elliptic curves, Springer, NY, 1986, p. 311.

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

Cf. A007519, A060953, A141194, A141195, A228228.

[p: p in PrimesUpTo(1223) | p mod 16 in {7, 11}];

Select[Prime@Range[200], MemberQ[{7, 11}, Mod[#, 16]] &]

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A094407 Primes of the form 16n+1.

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A141194 Primes of the form 16k+7.

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A141196 Primes of the form 16k+13.

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A228227 Primes congruent to {7, 11} mod 16.

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