A093012 -id:A093012 - cp's OEIS frontend

A091968 Primes congruent to 3 (mod 16).

3, 19, 67, 83, 131, 163, 179, 211, 227, 307, 419, 467, 499, 547, 563, 643, 659, 691, 739, 787, 883, 947, 1091, 1123, 1171, 1187, 1283, 1427, 1459, 1523, 1571, 1619, 1667, 1699, 1747, 1811, 1907, 1987, 2003, 2083, 2099, 2131, 2179, 2243, 2339, 2371, 2467

Offset: 1

Giovanni Teofilatto, Mar 14 2004

For any n, the equations x^4 - y^4 = a(n)*z^2 and x^4 - a(n)^2*y^4 = z^2 are not solvable in natural numbers. - Arkadiusz Wesolowski, Aug 15 2013

L. J. Mordell, Diophantine Equations, Ac. Press, p. 23.
Trygve Nagell, Introduction to Number Theory, Chelsea Publishing Company, NY, 1964, p. 230.

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

Cf. A092022, A093012.

Select[Prime@Range[400], Mod[ #, 16] == 3 &] (* Ray Chandler, Dec 06 2006 *)

is(n)=isprime(n) && n%16==3 \\ Charles R Greathouse IV, Jul 01 2016

More terms from Ray Chandler, Mar 15 2004

A092022 Numbers k such that 16k + 3 is prime.

Original entry on oeis.org

0, 1, 4, 5, 8, 10, 11, 13, 14, 19, 26, 29, 31, 34, 35, 40, 41, 43, 46, 49, 55, 59, 68, 70, 73, 74, 80, 89, 91, 95, 98, 101, 104, 106, 109, 113, 119, 124, 125, 130, 131, 133, 136, 140, 146, 148, 154, 158, 161, 166, 169, 175, 176, 178, 185, 188, 199, 200, 203, 206, 208

Offset: 1

Ray Chandler, Mar 15 2004

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A091968, A093012.

[n: n in [0..300] |IsPrime(16*n+3)]; // Vincenzo Librandi, Mar 28 2015

Select[Range[0, 208], PrimeQ[16# + 3] &] (* Ray Chandler, Mar 15 2004 *)

is(n)=isprime(16*n+3) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A091968(n)-3)/16. - Zak Seidov, Mar 28 2015

A163595 Numbers k such that prime(k) == 5 (mod 9).

Original entry on oeis.org

3, 9, 13, 17, 30, 32, 35, 39, 52, 55, 62, 64, 69, 76, 79, 81, 94, 97, 103, 109, 113, 119, 132, 135, 139, 154, 160, 165, 170, 173, 176, 185, 196, 201, 208, 212, 215, 220, 223, 225, 234, 239, 245, 248, 253, 265, 270, 277

Offset: 1

Juri-Stepan Gerasimov, Aug 01 2009

nonn

The asymptotic density of this sequence is 1/6 (by Dirichlet's theorem). - Amiram Eldar, Mar 02 2021

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A000040, A000720, A061240, A093012.

for n from 1 to 300 do p := ithprime(n) ; if (p mod 9 ) = 5 then printf("%d,",n) ; fi; od: # R. J. Mathar, Aug 01 2009
A163595 := proc(n) option remember ; local a; if n = 1 then 3 ; else for a from procname(n-1)+1 do if ithprime(a) mod 9 = 5 then return(a) ; fi; end do: end if; end proc: seq(A163595(n),n=1..100) ; # R. J. Mathar, Oct 10 2009

Select[Range[300],Mod[Prime[#],9]==5&]  (* Harvey P. Dale, Apr 25 2011 *)

A000040(a(n)) = A061240(n).

a(n) = A000720(A061240(n)).

cp's OEIS Frontend

A091968 Primes congruent to 3 (mod 16).

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A092022 Numbers k such that 16k + 3 is prime.

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Magma

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A163595 Numbers k such that prime(k) == 5 (mod 9).

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Maple

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