A176616
Primes of the form x^2 + 7*y^2, where x and y=x+1 are consecutive natural numbers.
Original entry on oeis.org
7, 29, 67, 191, 277, 379, 631, 947, 1129, 1327, 2017, 2557, 2851, 4561, 4951, 5779, 6217, 8647, 9181, 12721, 13367, 14029, 15401, 16111, 17579, 20707, 21529, 22367, 24091, 24977, 31627, 36857, 37951, 42487, 43661, 44851, 47279, 53629, 58997
Offset: 1
A285790 is an almost identical sequence.
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[ a: n in [0..250] | IsPrime(a) where a is 8*n^2+14*n+7 ] // Vincenzo Librandi, Apr 25 2010
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Select[Table[x^2+7(x+1)^2,{x,0,100}],PrimeQ] (* Harvey P. Dale, May 03 2024 *)
A176617
Primes of the form 14*k^2 + 26*k + 13.
Original entry on oeis.org
13, 53, 673, 881, 1117, 1381, 1993, 2341, 3121, 4013, 6133, 6733, 8017, 9413, 11717, 12541, 25801, 27017, 36313, 43793, 51973, 53693, 55441, 59021, 64601, 80713, 85021, 96281, 100981, 123517, 128833, 139801, 160073, 169181, 175393, 181717
Offset: 1
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[ a: n in [0..250] | IsPrime(a) where a is 14*n^2+26*n+13 ] // Vincenzo Librandi, Apr 25 2010
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Select[Table[14n^2+26n+13, {n,0,200}], PrimeQ] (* Harvey P. Dale, Jan 04 2011 *)
A176622
Primes of the form x^2 + 17*y^2, where x and y=x+1 are consecutive natural numbers.
Original entry on oeis.org
17, 157, 281, 4021, 8669, 10321, 14057, 16141, 37997, 58369, 71317, 78277, 80669, 93169, 109357, 112181, 117937, 136069, 176221, 179801, 187069, 198241, 213641, 225569, 237821, 285517, 299281, 318137, 393977, 410117, 443369, 507697, 513761
Offset: 1
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[a: n in [1..250]|IsPrime(a) where a is 18*n^2+34*n+17] // Vincenzo Librandi, Dec 04 2010
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Select[Table[18x^2+34x+17,{x,0,200}],PrimeQ] (* Harvey P. Dale, May 06 2017 *)
Constraint y=x+1 added to definition by
R. J. Mathar, May 04 2010
A176695
Primes of the form x^2 + 29*(x+1)^2.
Original entry on oeis.org
29, 1069, 4297, 7649, 18701, 21817, 34613, 45553, 52837, 60661, 63389, 71933, 77929, 81017, 90641, 107881, 111509, 122753, 155377, 168601, 187073, 201557, 264893, 369409, 376097, 438989, 476029, 498973, 579353, 674701, 711173, 767681
Offset: 1
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[ a: n in [0..250] | IsPrime(a) where a is 30*n^2+58*n+29 ] // Vincenzo Librandi, Apr 25 2010
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Select[Table[x^2 + 29(x + 1)^2, {x, 0, 200}], PrimeQ] (* Harvey P. Dale, Dec 12 2010 *)
A346948
Isolated single primes enclosed by six composites on hexagonal spiral board of odd numbers.
Original entry on oeis.org
211, 257, 277, 331, 509, 563, 587, 647, 653, 673, 683, 709, 751, 757, 839, 853, 919, 983, 997, 1087, 1117, 1123, 1163, 1283, 1433, 1447, 1493, 1531, 1579, 1637, 1733, 1777, 1889, 1913, 1973, 1993, 2179, 2207, 2251, 2273, 2287, 2333, 2357, 2399, 2447, 2467
Offset: 1
3 is not a term because four of the six neighbors (1, 5, 13, 15, 17 and 19) are primes.
211 is a term because 211 is a prime and all six neighbors (145, 147, 209, 213, 287 and 289) are composites.
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from sympy import isprime; from math import sqrt, ceil
def neib(m):
if m == 1: return [3, 5, 7, 9, 11, 13]
if m == 3: return [17, 19, 5, 1, 13, 15]
L = [m for i in range(6)]; n = int(ceil((3+sqrt(6*m + 3))/6)); x=6*n*n; y=12*n
a0 = x-18*n+15; a1 =x-16*n+11; a2 =x-14*n+9
a3 = x-y+7; a4 =x-10*n+5; a5 =x-8*n+3; a6 =x-6*n+1
p = 0 if m==a0 else 1 if m>a0 and ma1 and ma2 and ma3 and ma4 and ma5 and m
Showing 1-5 of 5 results.
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