A272075 -id:A272075 - cp's OEIS frontend

A272438 Primes of the form abs(-66n^3 + 3845n^2 - 60897n + 251831) in order of increasing nonnegative n.

251831, 194713, 144889, 101963, 65539, 35221, 10613, 8681, 23057, 32911, 38639, 40637, 39301, 35027, 28211, 19249, 8537, 3529, 16553, 30139, 43891, 57413, 70309, 82183, 92639, 101281, 107713, 111539, 112363, 109789, 103421, 92863, 77719, 57593, 32089, 811

Offset: 1

Robert Price, Apr 29 2016

nonn

			65539 is in this sequence since abs(-66*4^3 + 3845*4^2 - 60897*4 + 251831) = abs(-4224+61520-243588+251831) = 65539 is prime.

Robert Price, Table of n, a(n) for n = 1..3012
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.

n = Range[0, 100]; Select[-66n^3 + 3845n^2 - 60897n + 251831, PrimeQ[#] &]

A272437 Nonnegative numbers n such that abs(-66n^3 + 3845n^2 - 60897n + 251831) 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, 47, 49, 51, 54, 58, 65, 68, 70, 75, 76, 77, 82, 88, 89, 97, 99, 101, 102, 104, 109

Offset: 1

Robert Price, Apr 29 2016

nonn

46 is the smallest number not in this sequence.

			4 is in this sequence since abs(-66*4^3 + 3845*4^2 - 60897*4 + 251831) = abs(-4224+61520-243588+251831) = 65539 is prime.

Robert Price, Table of n, a(n) for n = 1..3012
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.

Select[Range[0, 109], PrimeQ[-66#^3 + 3845#^2 - 60897# + 251831] &]

is(n)=isprime(abs(66*n^3-3845*n^2+60897*n-251831)) \\ Charles R Greathouse IV, Feb 20 2017

A272444 Primes of the form abs(n^5 - 99n^4 + 3588n^3 - 56822n^2 + 348272n - 286397) in order of increasing nonnegative n.

Original entry on oeis.org

286397, 8543, 210011, 336121, 402851, 424163, 412123, 377021, 327491, 270631, 212123, 156353, 106531, 64811, 32411, 9733, 3517, 8209, 5669, 2441, 14243, 27763, 41051, 52301, 59971, 62903, 60443, 52561, 39971, 24251, 7963, 5227, 10429, 1409, 29531, 91673

Offset: 1

Robert Price, Apr 29 2016

nonn

			402851 is in this sequence since abs(4^5 - 99*4^4 + 3588*4^3 - 56822*4^2 + 348272*4 - 286397) = abs(1024-25344+229632-909152+1393088-286397) = 402851 is prime.

Robert Price, Table of n, a(n) for n = 1..2170
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.

n = Range[0, 100]; Select[n^5 - 99n^4 + 3588n^3 - 56822n^2 + 348272n - 286397, PrimeQ[#] &]

lista(nn) = for(n=0, nn, if(isprime(p=abs(n^5-99*n^4+3588*n^3-56822*n^2+348272*n-286397)), print1(p, ", "))); \\ Altug Alkan, Apr 29 2016

A272323 Nonnegative numbers n such that abs(82n^3 - 1228n^2 + 6130n - 5861) 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, 34, 37, 39, 41, 43, 47, 49, 50, 53, 54, 55, 59, 61, 63, 64, 67, 72, 73, 75, 76, 81, 84, 86, 87, 88, 89, 90, 92, 95, 97, 98, 102, 103, 104

Offset: 1

Robert Price, Apr 25 2016

nonn

32 is the smallest number not in this sequence.

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

Cf. A271980, A272030, A272074, A272075, A272160, A271144, A272285, A272324, A076808.

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

lista(nn) = for(n=0, nn, if(isprime(abs(82*n^3-1228*n^2+6130*n-5861)), print1(n, ", "))); \\ Altug Alkan, Apr 25 2016

A272410 Primes of the form abs(n^4 - 97n^3 + 3294n^2 - 45458n + 213589) in order of increasing nonnegative n.

Original entry on oeis.org

213589, 171329, 135089, 104323, 78509, 57149, 39769, 25919, 15173, 7129, 1409, 2341, 4451, 5227, 4951, 3881, 2251, 271, 1873, 4019, 6029, 7789, 9209, 10223, 10789, 10889, 10529, 9739, 8573, 7109, 5449, 3719, 2069, 673, 271, 541, 109, 1949, 5273, 10399, 17669

Offset: 1

Robert Price, Apr 30 2016

nonn

			78509 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.

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

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

A272443 Nonnegative numbers n such that abs(n^5 - 99n^4 + 3588n^3 - 56822n^2 + 348272n - 286397) 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, 48, 50, 51, 53, 57, 58, 59, 64, 67, 70, 75, 79, 80, 81, 89, 91, 92, 93, 96, 99

Offset: 1

Robert Price, Apr 29 2016

nonn

47 is the smallest number not in this sequence.

			4 is in this sequence since abs(4^5 - 99*4^4 + 3588*4^3 - 56822*4^2 + 348272*4 - 286397) = abs(1024-25344+229632-909152+1393088-286397) = 402851 is prime.

Robert Price, Table of n, a(n) for n = 1..2170
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.

Select[Range[0, 100], PrimeQ[#^5 - 99#^4 + 3588#^3 - 56822#^2 + 348272# - 286397] &]

lista(nn) = for(n=0, nn, if(isprime(abs(n^5-99*n^4+3588*n^3-56822*n^2+348272*n-286397)), print1(n, ", "))); \\ Altug Alkan, Apr 29 2016

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

Original entry on oeis.org

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[#] &]

A272077 Primes of the form abs(7k^2 - 371k + 4871) in order of increasing nonnegative values of k.

Original entry on oeis.org

4871, 4507, 4157, 3821, 3499, 3191, 2897, 2617, 2351, 2099, 1861, 1637, 1427, 1231, 1049, 881, 727, 587, 461, 349, 251, 167, 97, 41, 29, 43, 43, 29, 41, 97, 167, 251, 349, 461, 587, 727, 881, 1049, 1231, 1427, 1637, 1861, 2099, 2351, 2617, 2897, 3191

Offset: 1

Robert Price, Apr 19 2016

nonn

For k=0 to 23, this expression generates 24 primes that decrease from 4871 to 41. It generates duplicates and the absolute value is used to avoid negative terms. The same 24 primes but in reverse order are generated in the same range of the argument by 7*k^2+49*k+41, which produces neither duplicates nor negative values and is one of relatively few quadratics with at most two-digit coefficients that generate at least 20 primes in a row. We have: 7*(n-30)^2 + 49*(n-30) + 41 = 7*n^2 - 371*n + 4871. - Waldemar Puszkarz, Feb 02 2018

See also A298078, the values of 7*n^2-7*n-43, which also contains the same 24 primes without duplicates. - N. J. A. Sloane, Mar 10 2018

			4157 is in this sequence since 7*2^2 - 371*2 + 4871 = 28-742-4871 = 4157 is prime.

Robert Price, Table of n, a(n) for n = 1..3530
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

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

Cf. A271980, A272074, A272075, A272076, A298078.

Filtered(List([0..10^2],n->7*n^2-371*n+4871),IsPrime); # Muniru A Asiru, Feb 04 2018

select(isprime, [seq(7*n^2-371*n+4871, n=0..10^2)]); # Muniru A Asiru, Feb 04 2018

n = Range[0, 100]; Select[Abs[7n^2 - 371n + 4871], PrimeQ[#] &]

lista(nn) = for(n=0, nn, if(ispseudoprime(p=abs(7*n^2-371*n+4871)), print1(p, ", "))); \\ Altug Alkan, Apr 19 2016

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A272438 Primes of the form abs(-66n^3 + 3845n^2 - 60897n + 251831) in order of increasing nonnegative n.

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A272437 Nonnegative numbers n such that abs(-66n^3 + 3845n^2 - 60897n + 251831) is prime.

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A272444 Primes of the form abs(n^5 - 99n^4 + 3588n^3 - 56822n^2 + 348272n - 286397) in order of increasing nonnegative n.

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A272323 Nonnegative numbers n such that abs(82n^3 - 1228n^2 + 6130n - 5861) is prime.

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A272410 Primes of the form abs(n^4 - 97n^3 + 3294n^2 - 45458n + 213589) in order of increasing nonnegative n.

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A272443 Nonnegative numbers n such that abs(n^5 - 99n^4 + 3588n^3 - 56822n^2 + 348272n - 286397) is prime.

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

A272077 Primes of the form abs(7k^2 - 371k + 4871) in order of increasing nonnegative values of k.