A272030 -id:A272030 - cp's OEIS frontend

A267252 Primes of the form abs(103n^2 - 4707n + 50383) in order of increasing nonnegative n.

50383, 45779, 41381, 37189, 33203, 29423, 25849, 22481, 19319, 16363, 13613, 11069, 8731, 6599, 4673, 2953, 1439, 131, 971, 1867, 2557, 3041, 3319, 3391, 3257, 2917, 2371, 1619, 661, 503, 1873, 3449, 5231, 7219, 9413, 11813, 14419, 17231, 20249, 23473, 26903

Offset: 1

Robert Price, Apr 28 2016

This polynomial is a transformed version of the polynomial P(x) = 103*x^2 + 31*x - 3391 whose absolute value gives 43 distinct primes for -23 <= x <= 19, found by G. W. Fung in 1988. - Hugo Pfoertner, Dec 13 2019

			33203 is in this sequence since 103*4^2 - 4707*4 + 50383  = 1648-18828+50383 = 33203 is prime.

Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.

Robert Price, Table of n, a(n) for n = 1..3885
François Dress and Michel Olivier, Polynômes prenant des valeurs premières, Experimental Mathematics, Volume 8, Issue 4 (1999), 319-338.
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272118, A272159, A271143, A272284, A272323, A267069, A330363.

n = Range[0, 100]; Abs @ Select[103n^2 - 4707n + 50383 , PrimeQ[#] &]

lista(nn) = for(n=0, nn, if(isprime(p=abs(103*n^2-4707*n+50383)), print1(p, ", "))); \\ Altug Alkan, Apr 28 2016, corrected by Hugo Pfoertner, Dec 13 2019

Title corrected by Hugo Pfoertner, Dec 13 2019

A268200 Nonnegative numbers n such that abs(n^4 - 97n^3 + 3294n^2 - 45458n + 213589) is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 62, 65, 67, 70, 72, 73, 74, 75, 84, 85, 86, 90, 92

Offset: 1

Robert Price, Apr 30 2016

nonn

50 is the smallest number not in this sequence.

			4 is in this sequence since abs(4^4 - 97*4^3 + 3294*4^2 - 45458*4 + 213589) = abs(256-6208+52704-181832+213589) = 78509 is prime.

Robert Price, Table of n, a(n) for n = 1..2676
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266, A271980, A272030, A272074, A272075, A272160, A271144, A272285, A272401, A272438, A272444, A272410.

Select[Range[0, 100], PrimeQ[#^4 - 97#^3 + 3294#^2 - 45458# + 213589] &]

is(n)=isprime(abs(n^4-97*n^3+3294*n^2-45458*n+213589)) \\ Charles R Greathouse IV, Feb 20 2017

A272555 Primes of the form abs(1/(36)(n^6 - 126n^5 + 6217n^4 - 153066n^3 + 1987786n^2 - 13055316n + 34747236)) in order of increasing nonnegative n.

Original entry on oeis.org

965201, 653687, 429409, 272563, 166693, 98321, 56597, 32969, 20873, 15443, 13241, 12007, 10429, 7933, 4493, 461, 3583, 6961, 9007, 9157, 7019, 2423, 4549, 13553, 23993, 35051, 45737, 54959, 61613, 64693, 63421, 57397, 46769, 32423, 16193, 1091, 8443, 6271

Offset: 1

Robert Price, May 02 2016

nonn

			166693 is in this sequence since abs(1/(36)(4^6 - 126*4^5 + 6217*4^4 - 153066*4^3 + 1987786*4^2 - 13055316*4 + 34747236)) = abs((4096 - 129024 + 1591552 - 9796224 + 31804576 - 5222126 + 34747236)/36) = 166693 is prime.

Robert Price, Table of n, a(n) for n = 1..2128
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272159, A271143, A272284, A272302, A272437, A272443, A268200, A272554.

n = Range[0, 100]; Select[1/(36)(n^6 - 126n^5 + 6217n^4 - 153066n^3 + 1987786n^2 - 13055316n + 34747236), PrimeQ[#] &]

A272324 Primes of the form abs(82n^3 - 1228n^2 + 6130n - 5861) in order of increasing nonnegative n.

Original entry on oeis.org

5861, 877, 2143, 3691, 4259, 4339, 4423, 5003, 6571, 9619, 14639, 22123, 32563, 46451, 64279, 86539, 113723, 146323, 184831, 229739, 281539, 340723, 407783, 483211, 567499, 661139, 764623, 878443, 1003091, 1139059, 1286839, 1446923, 2005919, 2693363, 3229579

Offset: 1

Robert Price, Apr 25 2016

nonn

			4259 is in this sequence since 82*4^3 - 1228*4^2 + 6130*4 - 5861 = 5248-19648+24520-5861 = 4259 is prime.

Robert Price, Table of n, a(n) for n = 1..2659
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A076808, A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272118, A272159, A271143, A272284, A272323.

n = Range[0, 100]; Select[82n^3 - 1228n^2 + 6130n - 5861, PrimeQ[#] &]

A272325 Nonnegative numbers n such that n^4 + 853n^3 + 2636n^2 + 3536n + 1753 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 25, 26, 27, 30, 34, 37, 41, 43, 46, 50, 52, 53, 56, 59, 60, 61, 64, 66, 67, 68, 71, 76, 79, 81, 84, 87, 88, 89, 91, 92, 95, 96, 98, 99, 103, 106, 109, 118, 124, 126, 127, 128, 132

Offset: 1

Robert Price, Apr 25 2016

nonn

21 is the smallest number not in this sequence.

			4 is in this sequence since 4^4 + 853*4^3 + 2636*4^2 + 3536*4 + 1753 = 256+54592+42176+14144+1753 = 112921 is prime.

Robert Price, Table of n, a(n) for n = 1..2457
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272160, A271144, A272285, A272326, A076809.

Select[Range[0, 100], PrimeQ[#^4 + 853#^3 + 2636#^2 + 3536# + 1753] &]

lista(nn) = for(n=0, nn, if(isprime(n^4+853*n^3+2636*n^2+3536*n+1753), print1(n, ", "))); \\ Altug Alkan, Apr 25 2016

A272326 Primes of the form k^4 + 853k^3 + 2636k^2 + 3536*k + 1753 in order of increasing nonnegative k.

Original entry on oeis.org

1753, 8779, 26209, 59197, 112921, 192583, 303409, 450649, 639577, 875491, 1163713, 1509589, 1918489, 2395807, 2946961, 3577393, 4292569, 5097979, 5999137, 7001581, 8110873, 10672369, 15456403, 17324929, 19339909, 26321233, 38031841, 48822439, 66193219

Offset: 1

Robert Price, Apr 25 2016

nonn

			112921 is in this sequence since 4^4 + 853*4^3 + 2636*4^2 + 3536*4 + 1753 = 256+54592+42176+14144+1753 = 112921 is prime.

Robert Price, Table of n, a(n) for n = 1..2457
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272118, A272159, A271143, A272284, A272323, A272325, A076809.

n = Range[0, 100]; Select[n^4 + 853n^3 + 2636n^2 + 3536n + 1753, PrimeQ[#] &]

lista(nn) = for(n=0, nn, if(isprime(p=n^4+853*n^3+2636*n^2+3536*n+1753), print1(p, ", "))); \\ Altug Alkan, Apr 25 2016

A272554 Nonnegative numbers n such that abs(1/(36)(n^6 - 126n^5 + 6217n^4 - 153066n^3 + 1987786n^2 - 13055316n + 34747236)) is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 61, 62, 63, 64, 65, 66, 68, 69, 70, 73, 78

Offset: 1

Robert Price, May 02 2016

nonn

55 is the smallest number not in this sequence.

			4 is in this sequence since abs(1/(36)(4^6 - 126*4^5 + 6217*4^4 - 153066*4^3 + 1987786*4^2 - 13055316*4 + 34747236)) = abs((4096 - 129024 + 1591552 - 9796224 + 31804576 - 5222126 + 34747236)/36) = 166693 is prime.

Robert Price, Table of n, a(n) for n = 1..2128
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272160, A271144, A272285, A272401, A272438, A272444, A272410, A272555.

Select[Range[0, 100], PrimeQ[1/(36)(#^6 - 126#^5 + 6217#^4 - 153066#^3 + 1987786#^2 - 13055316# + 34747236)] &]

A272710 Primes of the form abs((1/4)*(n^5 - 133n^4 + 6729n^3 - 158379n^2 + 1720294n - 6823316)) in order of increasing nonnegative n.

Original entry on oeis.org

1705829, 1313701, 991127, 729173, 519643, 355049, 228581, 134077, 65993, 19373, 10181, 26539, 33073, 32687, 27847, 20611, 12659, 5323, 383, 3733, 4259, 1721, 3923, 12547, 23887, 37571, 53149, 70123, 87977, 106207, 124351, 142019, 158923, 174907, 189977

Offset: 1

Robert Price, May 04 2016

nonn

			519643 is in this sequence since abs(1/4 (n^5 - 133n^4 + 6729n^3 - 158379n^2 + 1720294n - 6823316)) = abs((1024 - 34048 + 430656 - 2534064 + 6881176 - 6823316)/4) = 519643 is prime.

Robert Price, Table of n, a(n) for n = 1..2328
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272159, A271143, A272284, A272302, A272437, A272443, A268200, A272554, A247163.

n = Range[0, 100]; Select[1/4 (n^5 - 133n^4 + 6729n^3 - 158379n^2 + 1720294n - 6823316), PrimeQ[#] &]

A247163 Nonnegative numbers n such that abs(1/4 (n^5 - 133n^4 + 6729n^3 - 158379n^2 + 1720294n - 6823316)) is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 59, 60, 61, 64, 67, 68, 69, 74, 75, 76

Offset: 1

Robert Price, May 04 2016

nonn

62 is the smallest number not in this sequence.

			4 is in this sequence since abs(1/4 (n^5 - 133n^4 + 6729n^3 - 158379n^2 + 1720294n - 6823316)) = abs((1024 - 34048 + 430656 - 2534064 + 6881176 - 6823316)/4) = 519643 is prime.

Robert Price, Table of n, a(n) for n = 1..2328
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272160, A271144, A272285, A272401, A272438, A272444, A272410, A272555, A272710.

Select[Range[0, 100], PrimeQ[1/4 (#^5 - 133#^4 + 6729#^3 - 158379#^2 + 1720294# - 6823316)] &]

A267069 Nonnegative numbers n such that abs(103n^2 - 4707n + 50383) is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 53, 54, 57, 59, 60, 61, 63, 64, 65, 66, 67, 69, 73, 74, 76, 77, 80

Offset: 1

Robert Price, Apr 28 2016

nonn

43 is the smallest number not in this sequence.

See A267252 for more information. - Hugo Pfoertner, Dec 13 2019

			4 is in this sequence since 103*4^2 - 4707*4 + 50383  = 1648-18828+50383 = 33203 is prime.

Robert Price, Table of n, a(n) for n = 1..3885
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272160, A271144, A272285, A267252.

Select[Range[0, 100], PrimeQ[103#^2 - 4707# + 50383 ] &]

lista(nn) = for(n=0, nn, if(isprime(abs(103*n^2-4707*n+50383)), print1(n, ", "))); \\ Altug Alkan, Apr 28 2016, corrected by Hugo Pfoertner, Dec 13 2019

Title corrected by Hugo Pfoertner, Dec 13 2019

cp's OEIS Frontend

A267252 Primes of the form abs(103*n^2 - 4707*n + 50383) in order of increasing nonnegative n.

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A268200 Nonnegative numbers n such that abs(n^4 - 97n^3 + 3294n^2 - 45458n + 213589) is prime.

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A272555 Primes of the form abs(1/(36)(n^6 - 126n^5 + 6217n^4 - 153066n^3 + 1987786n^2 - 13055316n + 34747236)) in order of increasing nonnegative n.

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A272324 Primes of the form abs(82n^3 - 1228n^2 + 6130n - 5861) in order of increasing nonnegative n.

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A272325 Nonnegative numbers n such that n^4 + 853n^3 + 2636n^2 + 3536n + 1753 is prime.

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A272326 Primes of the form k^4 + 853*k^3 + 2636*k^2 + 3536*k + 1753 in order of increasing nonnegative k.

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A272554 Nonnegative numbers n such that abs(1/(36)(n^6 - 126n^5 + 6217n^4 - 153066n^3 + 1987786n^2 - 13055316n + 34747236)) is prime.

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A272710 Primes of the form abs((1/4)*(n^5 - 133n^4 + 6729n^3 - 158379n^2 + 1720294n - 6823316)) in order of increasing nonnegative n.

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A267252 Primes of the form abs(103n^2 - 4707n + 50383) in order of increasing nonnegative n.

A272326 Primes of the form k^4 + 853k^3 + 2636k^2 + 3536*k + 1753 in order of increasing nonnegative k.

A267069 Nonnegative numbers n such that abs(103n^2 - 4707n + 50383) is prime.