A058077 -id:A058077 - cp's OEIS frontend

A125550 a(n) = C(prime(n+2), prime(n)).

10, 35, 462, 1716, 12376, 27132, 100947, 20030010, 7888725, 38608020, 1121099408, 6096454, 10737573, 19499099620, 1119487075980, 2944827765, 6522361560, 461738052776, 170230452, 26088783435

Offset: 1

Artur Jasinski, Jan 01 2007

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A058077.

Table[Binomial[Prime[x + 2], Prime[x]], {x, 1, 20}]
Binomial[Last[#],First[#]]&/@Partition[Prime[Range[50]],3,1] (* Harvey P. Dale, Oct 29 2013 *)

A060604 a(n) = binomial(prime(n), n) where prime(n) = n-th prime.

Original entry on oeis.org

2, 3, 10, 35, 462, 1716, 19448, 75582, 817190, 20030010, 84672315, 1852482996, 17620076360, 78378960360, 751616304549, 14844575908435, 277508869722315, 1312251244423350, 24151581961607100, 225368761961739396, 1084741953178481928, 19639369867938409940

Offset: 1

Labos Elemer, Apr 13 2001

nonn

Harry J. Smith, Table of n, a(n) for n=1..100

Cf. A058077, A060497.

Array[Binomial[Prime@ #, #] &, 20] (* Michael De Vlieger, Feb 18 2017 *)

a(n) = { binomial(prime(n), n) } \\ Harry J. Smith, Jul 07 2009

A126993 a(n) = binomial(prime(n+3), prime(n)).

Original entry on oeis.org

21, 165, 1287, 19448, 75582, 1144066, 51895935, 141120525, 6107086800, 7898654920, 15338678264, 5178066751, 266783135710, 109712808959985, 22512762077400, 97862516286480, 12802736917880, 18385569737808

Offset: 1

Artur Jasinski, Jan 01 2007

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A058077, A125550, A126994, A126995, A126996, A126997, A126998.

[Binomial(NthPrime(n+3), NthPrime(n)): n in [1..20]]; // G. C. Greubel, May 29 2019

Table[Binomial[Prime[n+3], Prime[n]], {x, 1, 20}]

vector(20, n, binomial(prime(n+3), prime(n))) \\ G. C. Greubel, May 29 2019

[binomial(nth_prime(n+3), nth_prime(n)) for n in (1..20)] # G. C. Greubel, May 29 2019

A126995 a(n) = binomial(prime(n+2), 3).

Original entry on oeis.org

1, 10, 35, 165, 286, 680, 969, 1771, 3654, 4495, 7770, 10660, 12341, 16215, 23426, 32509, 35990, 47905, 57155, 62196, 79079, 91881, 113564, 147440, 166650, 176851, 198485, 209934, 234136, 333375, 366145, 419220, 437989, 540274, 562475, 632710, 708561, 762355

Offset: 0

Artur Jasinski, Jan 01 2007

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A008837, A058077, A125550, A126993, A126994, A126996, A126997, A126998.

[Binomial(NthPrime(n), 3): n in [3..40]]; // Vincenzo Librandi, May 10 2017

Table[Binomial[Prime[n + 2], Prime[2]], {n, 1, 40}]
Table[Binomial[Prime[n], 3], {n, 3, 40}] (* Vincenzo Librandi, May 10 2017 *)

a(n)=binomial(prime(n+2),3) \\ Charles R Greathouse IV, May 10 2017

[binomial(nth_prime(n+2), 3) for n in (1..40)] # G. C. Greubel, May 29 2019

a(n) ~ (n log n)^3 / 6. - Charles R Greathouse IV, May 10 2017

Missing n=0 term added by N. J. A. Sloane, May 17 2020

A126996 a(n) = binomial(prime(3+n), prime(3)).

Original entry on oeis.org

1, 21, 462, 1287, 6188, 11628, 33649, 118755, 169911, 435897, 749398, 962598, 1533939, 2869685, 5006386, 5949147, 9657648, 13019909, 15020334, 22537515, 29034396, 41507642, 64446024, 79208745, 87541245, 106308566, 116828271, 140364532, 254231775

Offset: 0

Artur Jasinski, Jan 01 2007

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A008837, A058077, A125550, A126993, A126995, A126997, A126998.

[Binomial(NthPrime(n+3), 5): n in [0..30]]; // Vincenzo Librandi, May 21 2019

Table[Binomial[Prime[n + 3], Prime[3]], {n, 0, 30}]
Binomial[Prime[Range[3,40]],5] (* Harvey P. Dale, Mar 20 2021 *)

vector(30, n, binomial(prime(n+3), 5)) \\ G. C. Greubel, May 29 2019

[binomial(nth_prime(n+3), 5) for n in (1..30)] # G. C. Greubel, May 29 2019

Missing n=0 term added by N. J. A. Sloane, May 17 2020

A126997 a(n) = binomial(prime(4+n), prime(4)).

Original entry on oeis.org

1, 330, 1716, 19448, 50388, 245157, 1560780, 2629575, 10295472, 22481940, 32224114, 62891499, 154143080, 341149446, 436270780, 869648208, 1329890705, 1629348612, 2898753715, 4151918628, 6890268572, 12846240784, 17199613200, 19813501785, 26075972546, 29796772356, 38620298376

Offset: 0

Artur Jasinski, Jan 01 2007

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A058077, A125550, A126993, A126993, A008837, A126995, A126996, A126998.

[Binomial(NthPrime(n+4), 7): n in [1..30]]; // Vincenzo Librandi, May 21 2019

Table[Binomial[Prime[n + 4], Prime[4]], {n, 1, 30}]

vector(30, n, binomial(prime(n+4), prime(4)) ) \\ G. C. Greubel, May 29 2019

[binomial(nth_prime(n+4), 7) for n in (1..30)] # G. C. Greubel, May 29 2019

Terms a(24) onward added by G. C. Greubel, May 30 2019

Missing n=0 term added by N. J. A. Sloane, May 17 2020

A126998 a(n) = binomial(prime(n+5), prime(5)).

Original entry on oeis.org

1, 78, 12376, 75582, 1352078, 34597290, 84672315, 854992152, 3159461968, 5752004349, 17417133617, 76223753060, 279871768995, 418094152866, 1285063345176, 2560547383576, 3558497368608, 9036996468045, 16141841823510, 36519676207704, 99468442390512, 158940114100040

Offset: 0

Artur Jasinski, Jan 01 2007

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A058077, A125550, A126993, A126993, A008837, A126995, A126996, A126997.

[Binomial(NthPrime(n+5), NthPrime(5)): n in [1..30]]; // G. C. Greubel, May 29 2019

Table[Binomial[Prime[n+5], Prime[5]], {n, 1, 30}]

vector(30, n, binomial(prime(n+5), prime(5)) ) \\ G. C. Greubel, May 29 2019

[binomial(nth_prime(n+5), nth_prime(5)) for n in (1..30)] # G. C. Greubel, May 29 2019

Terms a(19) onward added by G. C. Greubel, May 30 2019

Missing n=0 term added by N. J. A. Sloane, May 17 2020

A126994 a(n) = binomial(prime(n+5), prime(n)).

Original entry on oeis.org

1, 78, 680, 11628, 245157, 34597290, 206253075, 15905368710, 244662670200, 960566918220, 4568648125690, 462525733568080, 8964377427999630, 6236646703759395, 972963730453314600, 5300174441392685400

Offset: 0

Artur Jasinski, Jan 01 2007

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A058077, A125550, A126993, A126995, A126996, A126997, A126998.

[Binomial(NthPrime(n+5), NthPrime(n)): n in [1..20]]; // G. C. Greubel, May 29 2019

Table[Binomial[Prime[n+5], Prime[n]], {n, 0, 20}]

vector(20, n, binomial(prime(n+5), prime(n))) \\ G. C. Greubel, May 29 2019

[binomial(nth_prime(n+5), nth_prime(n)) for n in (1..20)] # G. C. Greubel, May 29 2019

Missing n=0 term added by N. J. A. Sloane, May 17 2020

A080911 a(n) = binomial(n!,(n-1)!).

Original entry on oeis.org

1, 2, 15, 134596, 10872202353646160680764975

Offset: 1

Labos Elemer, Apr 01 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 1..7

Cf. A000142, A037293, A066526, A058077.

Table[Binomial[n!, (n-1)!], {n, 1, 7}] (* Vaclav Kotesovec, Nov 13 2014 *)

A058078 Greatest common divisor of two binomial coefficients formed from consecutive primes: a(n) = gcd(C(prime(n+2), prime(n+1)), C(prime(n+1), prime(n))).

Original entry on oeis.org

1, 1, 3, 6, 2, 1, 1, 35, 15, 3, 2, 1, 3, 5, 14, 6, 6, 7, 1, 1, 5, 4, 4, 15, 3, 1, 2, 2, 55, 5, 4, 3, 1, 1, 3, 84, 1, 1, 28, 10, 3, 3, 1, 1, 1, 221, 3, 6, 2, 7, 3, 15, 231, 21, 7, 1, 5, 70, 3, 1, 1292, 35, 1, 3, 15, 24, 7, 1, 6, 7, 1, 3, 42, 5, 1, 231, 35, 1, 143, 2, 5, 1, 1, 7, 14, 1, 45, 3

Offset: 1

Labos Elemer, Nov 13 2000

nonn

			n = 8, a(8) = gcd(C(prime(10), prime(9)), C(prime(9), prime(8))) = gcd(C(29, 23), C(23, 19)) = gcd(8855, 475020) = gcd(5*7*11*23, 2^2*3^2*5*7*13*29) = 5*7 = 35.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A058077, A334906.

A058078:=n->gcd(binomial(ithprime(n+2),ithprime(n+1)), binomial(ithprime(n+1), ithprime(n))); seq(A058078(n), n=1..100); # Wesley Ivan Hurt, Apr 01 2014

GCD[Binomial[Last[#],#[[2]]],Binomial[#[[2]],First[#]]]&/@ Partition[ Prime[ Range[90]],3,1] (* Harvey P. Dale, May 05 2011 *)

a(n,p=prime(n))=my(q=nextprime(p+1),r=nextprime(q+1)); gcd(binomial(r,q), binomial(q,p)) \\ Charles R Greathouse IV, Nov 18 2015

a(n) = gcd(f(n+1), f(n)) where f(n) = binomial(prime(n+1), prime(n)). - Joerg Arndt, Apr 05 2014

Edited by Wolfdieter Lang, Apr 16 2014

cp's OEIS Frontend

A125550 a(n) = C(prime(n+2), prime(n)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A060604 a(n) = binomial(prime(n), n) where prime(n) = n-th prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A126993 a(n) = binomial(prime(n+3), prime(n)).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

A126995 a(n) = binomial(prime(n+2), 3).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Formula

Extensions

A126996 a(n) = binomial(prime(3+n), prime(3)).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Extensions

A126997 a(n) = binomial(prime(4+n), prime(4)).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Extensions

A126998 a(n) = binomial(prime(n+5), prime(5)).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Extensions

A126994 a(n) = binomial(prime(n+5), prime(n)).

Views