A245042
Primes of the form (k^2+4)/5.
Original entry on oeis.org
17, 73, 89, 193, 337, 521, 953, 1009, 1249, 1657, 2377, 2833, 3329, 3433, 4441, 4561, 5849, 6553, 7297, 8081, 8737, 9769, 11617, 12401, 12601, 13417, 15569, 16937, 17881, 18121, 20353, 21649, 27529, 28729, 29033, 30577, 33457, 35449, 36809, 46273, 49801
Offset: 1
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Select[(Range[500]^2+4)/5,PrimeQ] (* Harvey P. Dale, Jul 13 2014 *)
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import sympy
L = (k**2 + 4 for k in range(10**3))
[n//5 for n in L if n % 5 == 0 and sympy.ntheory.isprime(n//5)]
A245045
Primes of the form (k^2+2)/6.
Original entry on oeis.org
3, 11, 17, 43, 67, 113, 131, 193, 241, 353, 523, 641, 683, 1291, 1601, 1667, 1873, 2017, 2243, 2731, 3083, 3361, 3851, 4483, 4817, 4931, 5281, 5521, 7211, 8363, 8513, 8971, 9283, 9923, 10753, 11971, 13633, 16433, 17713, 18371, 18593, 19267, 21841, 22571
Offset: 1
When k=4, (k^2+2)/6 = 3 is prime, so 4 is a member of the sequence. since putting k = 0, 1, 2, or 3 does not give a prime, so 4 is the first term.
A154618
Triangle read by rows: integer values of T(n,m) = (4*m*n+2*m+2*n-3)/3.
Original entry on oeis.org
7, 15, 17, 39, 29, 55, 27, 61, 95, 43, 81, 119, 37, 83, 129, 175, 57, 107, 157, 207, 47, 105, 163, 221, 279, 71, 133, 195, 257, 319, 57, 127, 197, 267, 337, 407, 85, 159, 233, 307, 381, 455, 67, 149, 231, 313, 395, 477, 559, 99, 185, 271, 357, 443, 529, 615, 77
Offset: 1
The sequence contains the integers selected from the full table:
5/3;
11/3,7;
17/3,31/3,15;
23/3,41/3,59/3,77/3;
29/3,17,73/3,95/3,39;
35/3,61/3,29,113/3,139/3,55;
41/3,71/3,101/3,131/3,161/3,191/3,221/3;
47/3,27,115/3,149/3,61,217/3,251/3,95;
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Select[Flatten[Table[(4*m*n+2*m+2*n-3)/3,{m,30},{n,m}]],IntegerQ] (* Harvey P. Dale, Jun 10 2015 *)
Keyword:tabl removed, appearance of fractions clarified by
R. J. Mathar, Oct 16 2009
A154632
Odd primes p such that (4*p^2-8*p-9)/3 is a prime.
Original entry on oeis.org
5, 17, 23, 41, 59, 71, 89, 149, 197, 233, 239, 347, 359, 401, 419, 449, 563, 683, 761, 773, 827, 887, 971, 977, 1049, 1061, 1097, 1193, 1277, 1373, 1439, 1553, 1571, 1787, 1871, 1877, 1931, 2069, 2267, 2273, 2381, 2417, 2447, 2687, 2699, 2777, 2843, 2957
Offset: 1
For p=5, (4*p^2-8*p-9)/3 = 17; for p=149, (4*p^2-8*p-9)/3 = 29201.
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a := proc (n) if isprime(n) = true and type((4/3)*n^2-(8/3)*n-3, integer) = true and isprime((4/3)*n^2-(8/3)*n-3) = true then n else end if end proc: seq(a(n), n = 2 .. 4000); # Emeric Deutsch, Jan 20 2009
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Select[Prime[Range[2, 500]], PrimeQ[(4 #^2 - 8 # - 9)/3] &] (* Harvey P. Dale, May 20 2012 *)
A157417
Primes of the form floor((4*n^2-8*n-9)/3).
Original entry on oeis.org
7, 17, 29, 43, 61, 103, 157, 257, 337, 641, 701, 829, 967, 1117, 1277, 1361, 1447, 1723, 2129, 2237, 2347, 3067, 3329, 3463, 4177, 4327, 4481, 4637, 4957, 5981, 6343, 6529, 6907, 7297, 7901, 8317, 9181, 9403, 9629, 9857, 10321, 11527, 11777, 12541, 13063
Offset: 1
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[a: n in [3..100] | IsPrime(a) where a is Floor((4*n^2-8*n-9)/3)]; // Vincenzo Librandi, Mar 21 2013
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Select[Table[Floor[(4 n^2 - 8 n - 9)/3], {n, 3, 100}], PrimeQ] (* Vincenzo Librandi, Mar 21 2013 *)
A242930
Primes of the form (k^2+7)/11.
Original entry on oeis.org
37, 53, 193, 373, 421, 673, 1061, 2213, 2753, 3637, 4481, 5237, 5413, 7333, 7541, 8513, 8737, 9781, 11393, 12853, 14401, 15733, 17761, 19237, 21121, 25153, 25537, 27701, 29537, 34273, 34721, 39841, 42533, 47653, 50593, 51137
Offset: 1
Showing 1-6 of 6 results.
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