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
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[Binomial(NthPrime(n+3), NthPrime(n)): n in [1..20]]; // G. C. Greubel, May 29 2019
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Table[Binomial[Prime[n+3], Prime[n]], {x, 1, 20}]
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vector(20, n, binomial(prime(n+3), prime(n))) \\ G. C. Greubel, May 29 2019
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[binomial(nth_prime(n+3), nth_prime(n)) for n in (1..20)] # G. C. Greubel, May 29 2019
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
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[Binomial(NthPrime(n+3), 5): n in [0..30]]; // Vincenzo Librandi, May 21 2019
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Table[Binomial[Prime[n + 3], Prime[3]], {n, 0, 30}]
Binomial[Prime[Range[3,40]],5] (* Harvey P. Dale, Mar 20 2021 *)
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vector(30, n, binomial(prime(n+3), 5)) \\ G. C. Greubel, May 29 2019
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[binomial(nth_prime(n+3), 5) for n in (1..30)] # G. C. Greubel, May 29 2019
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
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[Binomial(NthPrime(n+4), 7): n in [1..30]]; // Vincenzo Librandi, May 21 2019
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Table[Binomial[Prime[n + 4], Prime[4]], {n, 1, 30}]
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vector(30, n, binomial(prime(n+4), prime(4)) ) \\ G. C. Greubel, May 29 2019
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[binomial(nth_prime(n+4), 7) for n in (1..30)] # G. C. Greubel, May 29 2019
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
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[Binomial(NthPrime(n+5), NthPrime(5)): n in [1..30]]; // G. C. Greubel, May 29 2019
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Table[Binomial[Prime[n+5], Prime[5]], {n, 1, 30}]
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vector(30, n, binomial(prime(n+5), prime(5)) ) \\ G. C. Greubel, May 29 2019
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[binomial(nth_prime(n+5), nth_prime(5)) for n in (1..30)] # G. C. Greubel, May 29 2019
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
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[Binomial(NthPrime(n+5), NthPrime(n)): n in [1..20]]; // G. C. Greubel, May 29 2019
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Table[Binomial[Prime[n+5], Prime[n]], {n, 0, 20}]
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vector(20, n, binomial(prime(n+5), prime(n))) \\ G. C. Greubel, May 29 2019
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[binomial(nth_prime(n+5), nth_prime(n)) for n in (1..20)] # G. C. Greubel, May 29 2019
A262248
Number of intersections of diagonals in the interior of a regular p-gon where p is the n-th prime.
Original entry on oeis.org
0, 0, 5, 35, 330, 715, 2380, 3876, 8855, 23751, 31465, 66045, 101270, 123410, 178365, 292825, 455126, 521855, 766480, 971635, 1088430, 1502501, 1837620, 2441626, 3464840, 4082925, 4421275, 5160610, 5563251, 6438740, 10334625, 11716640, 14043870
Offset: 1
For prime(2)=3, there is no intersection of diagonals in the interior of a regular triangle, so a(2)=0.
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[(NthPrime(n)^4-6*(NthPrime(n)^3)+11*NthPrime(n)^2- 6*NthPrime(n))/24: n in [1..40]]; // Vincenzo Librandi, Sep 17 2015
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Table[(Prime[n]^4 - 6 (Prime[n]^3) + 11 Prime[n]^2 - 6 Prime[n])/24, {n, 50}] (* Vincenzo Librandi, Sep 17 2015 *)
(#^4-6#^3+11#^2-6#)/24&/@Prime[Range[40]] (* Harvey P. Dale, Jun 17 2022 *)
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a(n) = my(p=prime(n)); p*(p^3 - 6*p^2 + 11*p - 6)/24;
vector(40, n, a(n))
Showing 1-6 of 6 results.
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