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 1-6 of 6 results.

A133529 Sum of squares of three consecutive primes.

Original entry on oeis.org

38, 83, 195, 339, 579, 819, 1179, 1731, 2331, 3171, 4011, 4899, 5739, 6867, 8499, 10011, 11691, 13251, 14859, 16611, 18459, 21051, 24219, 27531, 30219, 32259, 33939, 36099, 40779, 46059, 52059, 55251, 60291, 64323, 69651, 74019, 79107, 84387, 89859, 94731, 101283
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Comments

It is easy to see that all terms > 83 are divisible by 3.
Likewise all terms except 38 are congruent to 3 (mod 8). - Franklin T. Adams-Watters, Jun 17 2015

Examples

			a(1)=38 because 2^2 + 3^2 + 5^2 = 38.

Links

Crossrefs

Cf. A034963, A133524-A133528, A133530-A133533.

Programs

  • Magma
    [&+[ NthPrime(n+i)^2 :  i in [0..2]] : n in [1..20]]; // K. D. Bajpai, Jun 17 2015
  • Mathematica
    a = 2; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[50]]^2, 3, 1] (* Vincenzo Librandi, Jun 18 2015 *)
  • PARI
    for( n= 1, 100,  k= sum(i=n, n+2, prime(i)^2) ; print1(k, ", ")) \\ K. D. Bajpai, Jun 17 2015

Formula

a(n) = A069484(n) + A001248(n+2). - Michel Marcus, Nov 08 2013

Extensions

a(38)-a(41) from K. D. Bajpai, Jun 18 2015

A133530 Sum of third powers of three consecutive primes.

Original entry on oeis.org

160, 495, 1799, 3871, 8441, 13969, 23939, 43415, 66347, 104833, 149365, 199081, 252251, 332207, 458079, 581237, 733123, 885655, 1047691, 1239967, 1453843, 1769795, 2189429, 2647943, 3035701, 3348071, 3612799, 3962969, 4786309
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=160 because 2^3+3^3+5^3=160.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133531, A133532, A133533.

Programs

  • Mathematica
    a = 3; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]

Formula

a(n) = A133534(n) + A030078(n+2). - Michel Marcus, Nov 08 2013

A133528 Sum of sixth powers of four consecutive primes.

Original entry on oeis.org

134067, 1905564, 6731644, 30853588, 77781820, 224046148, 814042660, 1677408772, 4196089300, 8798157652, 14524697380, 24416409028, 44015043748, 81445473148, 126644484460, 206323651300, 312259574092, 421413266740
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=134067 because 2^6+3^6+5^6+7^6=134067.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527.

Programs

  • Mathematica
    a = 6; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a, {n, 1, 100}]

Formula

a(n) = A133533(n) + A030516(n+3). - Michel Marcus, Nov 08 2013

A133531 Sum of fourth powers of three consecutive primes.

Original entry on oeis.org

722, 3107, 17667, 45603, 126723, 242403, 493683, 1117443, 1910643, 3504963, 5623443, 8118723, 11124243, 16188963, 24887523, 33853683, 46114323, 59408643, 73961043, 92760003, 114806643, 149150643, 198729843, 255331923, 305140563
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=722 because 2^4+3^4+5^4=722.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133532, A133533.

Programs

  • Mathematica
    a = 4; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]

Formula

a(n) = A133535(n) + A030514(n+2). - Michel Marcus, Nov 09 2013

A133532 Sum of fifth powers of three consecutive primes.

Original entry on oeis.org

3400, 20175, 180983, 549151, 1952201, 4267249, 10332299, 29423591, 55576643, 118484257, 213829309, 332208601, 492209651, 794548943, 1362464799, 1977716093, 2909645707, 3998950759, 5227426051, 6954357343, 9089168635
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=3400 because 2^5+3^5+5^5=3400.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133533.

Programs

  • Mathematica
    a = 5; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
Total[#^5]&/@Partition[Prime[Range[30]],3,1] (* Harvey P. Dale, May 26 2011 *)

Formula

a(n) = A133536(n) + A050997(n+2). - Michel Marcus, Nov 09 2013

A176613 Smallest prime p of three consecutive primes such that the sum of their n-th powers is prime, or 0 if such a prime does not exist.

Original entry on oeis.org

2, 5, 3, 23, 0, 11, 0, 5, 0, 23, 3, 137, 0, 5, 3, 89, 0, 71, 0, 17, 0, 23, 0, 23, 3, 131, 3, 419, 0, 31, 0, 859, 0, 31, 0, 127, 0, 11, 0, 359, 0, 31, 0, 347, 0, 509, 0, 137, 0, 193, 0, 769, 0, 23, 0, 17
Offset: 0

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 21 2010

Keywords

Comments

Let p = prime(i), q = prime(i+1), r = prime(i+2).
(*) p^n + q^n + r^n has to be a prime.
When n is even and p > 3, then (*) is composite because primes greater than 3 are either of form 6k-1 or 6k+1 for some k. Hence, squares (or any even power) of such a prime has the form 6k+1. Adding three such even powers will produce a number of the form 6k+3, which is divisible by 3.
When n is even and p = 3, sequence A160773 gives the even n for which 3^n + 5^n + 7^n is prime.

Examples

			5 + 7 + 11 = 23 = prime(9); 3^2 + 5^2 + 7^2 = 83 = prime(23); 23^3 + 29^3 + 31^3 = 66347 = prime(6616).

Links

Crossrefs

Cf. A133530, A133531, A133532, A133533, A160773.

Programs

  • Maple
    f:= proc(n) local p,q,r;
  if n::even then
    if isprime(3^n+5^n+7^n) then return 3
    else return 0
    fi
  fi;
  p:= 2: q:= 3: r:= 5:
  while not isprime(p^n + q^n + r^n) do
    p:= q; q:= r; r:= nextprime(r)
  od;
  p
end proc:
f(0):= 2:
map(f, [$0..100]);

Extensions

a(0) term added by T. D. Noe, Nov 23 2010
Showing 1-6 of 6 results.

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