A091968
Primes congruent to 3 (mod 16).
Original entry on oeis.org
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
- L. J. Mordell, Diophantine Equations, Ac. Press, p. 23.
- Trygve Nagell, Introduction to Number Theory, Chelsea Publishing Company, NY, 1964, p. 230.
A093012
Numbers k such that prime(k) == 3 (mod 16).
Original entry on oeis.org
2, 8, 19, 23, 32, 38, 41, 47, 49, 63, 81, 91, 95, 101, 103, 117, 120, 125, 131, 138, 153, 161, 182, 188, 193, 195, 208, 225, 232, 241, 248, 256, 262, 266, 272, 280, 292, 300, 304, 314, 317, 321, 327, 334, 346, 351, 365, 370, 376, 385, 394, 409, 410, 414, 427
Offset: 1
-
[n: n in [1..450]|(NthPrime(n) mod 16) eq 3] // G. C. Greubel, Feb 05 2019
-
Select[Range[430], Mod[Prime[ # ], 16] == 3 &] (* Ray Chandler, Nov 06 2006 *)
-
{isok(n) = Mod(prime(n), 16)==3};
for(n=1, 450, if(isok(n)==1, print1(n, ", "), 0)) \\ G. C. Greubel, Feb 05 2019
A123990
Numbers k for which 16*k+1, 16*k+3, 16*k+7, 16*k+13 and 16*k+15 are primes.
Original entry on oeis.org
1, 7771, 18166, 21691, 26146, 26356, 46801, 69046, 75916, 91516, 111406, 122716, 156196, 171436, 175726, 177316, 201571, 219316, 222706, 259951, 282826, 355531, 426796, 433621, 435301, 438976, 440056, 524371, 560461, 585166, 605506, 608026
Offset: 1
-
Select[Range[10^6], And @@ PrimeQ /@ ({1, 3, 7, 13, 15} + 16#) &] (* Ray Chandler, Dec 06 2006 *)
A123992
Numbers k such that 16*k+1, 16*k+3 and 16*k+13 are primes.
Original entry on oeis.org
1, 40, 106, 133, 250, 265, 271, 280, 295, 313, 418, 580, 691, 736, 748, 826, 946, 1231, 1240, 1435, 1471, 1561, 1756, 2023, 2035, 2038, 2101, 2575, 2728, 2878, 2926, 3268, 3400, 3451, 3688, 3715, 3883, 4213, 4306, 4726, 4936, 5080, 5398, 5761, 5908, 6046
Offset: 1
-
a:=proc(n) if isprime(16*n+1)=true and isprime(16*n+3)=true and isprime(16*n+13)=true then n else fi end: seq(a(n),n=1..5000); # Emeric Deutsch, Nov 03 2006
-
Select[Range[6100], And @@ PrimeQ /@ ({1, 3, 13} + 16#) &] (* Ray Chandler, Nov 05 2006 *)
A123997
Numbers k for which 16*k+1, 16*k+3 and 16*k+15 are primes.
Original entry on oeis.org
1, 133, 166, 208, 313, 418, 616, 691, 718, 1336, 1441, 1573, 1588, 1756, 2083, 2308, 2533, 2926, 2986, 3688, 3766, 3883, 4036, 4096, 4201, 4663, 5311, 5626, 5908, 6181, 7018, 7456, 7771, 7798, 8188, 8881, 9196, 9343, 9388, 9826, 10108, 10123, 10528
Offset: 1
-
Select[Range[11000], And @@ PrimeQ /@ ({1, 3, 15} + 16#) &] (* Ray Chandler, Nov 05 2006 *)
A153348
Numbers n such that 16*n+3 is not prime.
Original entry on oeis.org
2, 3, 6, 7, 9, 12, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 28, 30, 32, 33, 36, 37, 38, 39, 42, 44, 45, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 90, 92, 93, 94
Offset: 1
Triangle begins:
*;
*,*;
*,2,*;
*,*,*,*;
*,*,*,6,*;
*,*.*,*,*,*;
*,*,*,*,*,12,*;
3,*,*,*,*,*,*,*;
*,*,*,*,*,*,*,20,*;
*,*,9,*,*,*,*,*,*,*;
*,7,*,*,*,*,*,*,*,30,*;
*,*,*,*,17,*,*,*,*,*,*,*;
where * marks the non-integer values of (2*h*k + k + h - 1)/8 with h >= k >= 1.
Showing 1-6 of 6 results.
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