cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A273462 Rounded variance of the first n primes, for n > 1.

Original entry on oeis.org

0, 2, 5, 13, 19, 31, 41, 56, 81, 103, 136, 171, 201, 235, 280, 335, 384, 444, 505, 560, 626, 693, 772, 869, 966, 1055, 1145, 1229, 1314, 1447, 1578, 1719, 1849, 2008, 2156, 2313, 2479, 2644, 2818, 3000, 3171, 3372, 3560, 3748, 3925, 4142, 4398, 4651, 4890
Offset: 2

Views

Author

Andres Cicuttin, May 23 2016

Keywords

Links

Crossrefs

Cf. A075465, A075471, A272206.
Mean and variance of primes: A301273/A301274, A301275/A301276, A301277, A273462.

Programs

  • Mathematica
    Table[Round[Variance[Prime[Range[j]]]], {j, 2, 50}]
  • Sage
    round(variance(primes_first_n(n))) # Danny Rorabaugh, May 25 2016

Formula

a(n) = round(Sum_{i=1..n} (prime(i) - Sum_{j=1..n} prime(j)/n)^2/(n - 1)), n > 1.

A239941 Primes p which are floor of Root-mean-cube (RMC) of prime(n), prime(n+1) and prime(n+2).

Original entry on oeis.org

7, 53, 89, 223, 257, 1097, 6823, 10181, 12149, 14783, 15527, 20063, 22027, 29917, 30539, 40519, 42491, 43261, 50543, 51511, 57727, 65063, 68639, 72103, 97453, 99391, 100693, 108463, 108893, 110281, 111581, 113363, 116719, 149623, 153407, 154211, 155821, 193057
Offset: 1

Views

Author

K. D. Bajpai, Apr 03 2014

Keywords

Examples

			11, 13 and 17 are consecutive primes: sqrt(( 11^3 + 13^3 + 17^3)/3) = 53.044...: floor(53.044...) = 53, which is prime and appears in the sequence.
31, 37 and 41 are consecutive primes: sqrt(( 31^3 + 37^3 + 41^3)/3) = 223.13...: floor(223.13...) = 223, which is prime and appears in the sequence.

Links

Crossrefs

Cf. A000040, A075471, A088165, A240339.

Programs

  • Maple
    select(isprime, {seq(floor(sqrt(add(ithprime(n+i)^3, i=0..2)/3)), n=1..1000)})[]; # corrected by Georg Fischer, Sep 27 2024

A240339 Primes p which are floor of Root-Mean-Cube (RMC) of prime(n) and prime(n+1).

Original entry on oeis.org

59, 97, 1321, 1621, 2539, 3511, 4339, 4889, 5591, 6491, 6917, 9419, 10289, 11689, 16381, 18719, 19441, 23053, 23567, 28499, 41051, 47143, 64661, 65203, 67939, 71023, 82493, 89107, 94999, 98927, 106087, 114941, 117281, 120823, 135647, 139361, 144289, 154799
Offset: 1

Views

Author

K. D. Bajpai, Apr 04 2014

Keywords

Examples

			13 and 17 are consecutive primes: sqrt((13^3 + 17^3)/2) = 59.62382073: floor(59.62382073)= 59, which is prime and appears in the sequence.
19 and 23 are consecutive primes: sqrt((19^3 + 23^3)/2) = 97.53460923: floor(97.53460923)= 97, which is prime and appears in the sequence.

Links

Crossrefs

Cf. A000040, A075471, A088165, A239941.

Programs

  • Maple
    select(isprime, {seq(floor(sqrt((ithprime(n)^3 + ithprime(n+1)^3)/2)),n=1..1000)}); # corrected by Georg Fischer, Sep 27 2024
  • Mathematica
    Select[Floor[Sqrt[Mean[#]]]&/@(Partition[Prime[Range[600]],2,1]^3), PrimeQ] (* Harvey P. Dale, Sep 24 2014 *)

A240278 Primes p which are floor of Root-Mean-Square (RMS) of prime(n), prime(n+1) and prime(n+2).

Original entry on oeis.org

3, 5, 13, 19, 43, 47, 53, 83, 89, 103, 109, 131, 157, 167, 173, 193, 211, 229, 233, 257, 263, 313, 349, 353, 359, 373, 383, 389, 409, 443, 449, 463, 503, 563, 593, 607, 643, 647, 653, 677, 683, 691, 709, 733, 797, 823, 859, 883, 919, 941, 947, 971, 977, 983, 1013
Offset: 1

Views

Author

K. D. Bajpai, Apr 03 2014

Keywords

Examples

			11, 13 and 17 are consecutive primes: sqrt(( 11^2 + 13^2 + 17^2)/3) = 13.89244399: floor(13.89244399) = 13, which is prime and appears in the sequence.
17, 19 and 23 are consecutive  primes: sqrt(( 17^2 + 19^2 + 23^2)/3) = 19.82422760: floor(19.82422760) = 19, which is prime and appears in the sequence.
41, 43 and 47 are consecutive  primes: sqrt(( 41^2 + 43^2 + 47^2)/3) = 43.73785546: floor(43.73785546) = 43, which is prime and appears in the sequence.

Links

Crossrefs

Cf. A000040, A075471, A088165.

Programs

  • Maple
    a := proc(n) local c, b, d, e; c:=ithprime(n); b:=ithprime(n+1); d:=ithprime(n+2); e:=floor(sqrt((c^2+b^2+d^2)/3)); if isprime(e) then RETURN(e); fi; end: seq(a(n), n=1..500);
  • Mathematica
    Select[Floor[RootMeanSquare[#]]&/@Partition[Prime[Range[200]],3,1],PrimeQ] (* Harvey P. Dale, Mar 23 2018 *)
Showing 1-4 of 4 results.

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