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.

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A133561 Numbers n for which sum of squares of seven consecutive primes(n,n+1,n+2,n+3,n+4,n+5,n+6) is prime.

Original entry on oeis.org

3, 5, 6, 8, 9, 10, 14, 18, 19, 20, 21, 26, 32, 34, 37, 38, 39, 41, 44, 47, 49, 52, 53, 54, 59, 60, 63, 64, 66, 68, 70, 71, 75, 83, 88, 89, 91, 92, 97, 100, 107, 108, 110, 112, 113, 117, 122, 125, 128, 129, 131, 135, 141, 142, 150, 151, 157, 158, 165, 168, 169, 178, 183
Offset: 1

Views

Author

Artur Jasinski, Sep 16 2007

Keywords

Comments

For sum of squares of two consecutive primes only 2^2+3^2=13 is prime.
For sum of squares of three consecutive primes A133529 seems that only 83 belonging (checked for all n<1000000).
Sums of squares of four (and all even number) of consecutive primes are even numbers with exception n=1 but 2^2+3^2+5^2+7^2=87=3*29 is not prime.
Sums of squares of five of consecutive primes A133559.
Sums of squares of seven of consecutive primes A133562.

Examples

			a(3)=6 because prime(6)^2+prime(7)^2+prime(8)^2+prime(9)^2+prime(10)^2+prime(11)^2+prime(12)^2 = 13^2+17^2+19^2+23^2+29^2+31^2+37^2=4519 is prime.

Links

Crossrefs

Cf. A133538, A133559, A133562.

Programs

  • Maple
    select(n->isprime(add(ithprime(n+k)^2,k=0..6)),[$1..200]); # Muniru A Asiru, Jul 28 2018
  • Mathematica
    b = {}; a = 2; Do[k = Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a + Prime[n + 5]^a + Prime[n + 6]^a; If[PrimeQ[k], AppendTo[b, n]], {n, 1, 100}]; b
  • PARI
    is(n) = ispseudoprime(sum(i=0, 6, prime(n+i)^2)) \\ Felix Fröhlich, Jul 28 2018

A133562 Numbers which are the sum of the squares of seven consecutive primes.

Original entry on oeis.org

666, 1023, 1543, 2359, 3271, 4519, 6031, 7591, 9439, 11719, 14359, 17119, 20239, 23599, 27079, 31111, 35191, 39631, 45319, 51031, 56599, 62719, 68359, 74239, 82447, 90199, 98767, 107479, 118231, 129151, 141031, 151471, 162199, 173359
Offset: 1

Views

Author

Artur Jasinski, Sep 16 2007

Keywords

Comments

For primes in this sequence see A133560.
For sum of squares of two consecutive primes only 2^2 + 3^2 = 13 is prime.
For sum of squares of three consecutive primes A133529 it seems that only 83 is a prime (checked for all n < 1000000).
Sums of squares of four (and all even number) of consecutive primes are even numbers with exception n=1 but 2^2 + 3^2 + 5^2 + 7^2 = 87 = 3*29 is not prime.
For primes that are sums of squares of five consecutive primes see A133559.

Examples

			a(6) = 13^2 + 17^2 + 19^2 + 23^2 + 29^2 + 31^2 + 37^2 = 4519.

Links

Crossrefs

Cf. A133529, A133538, A133558, A133559, A133560, A133561.

Programs

  • Maple
    seq(add(ithprime(n+k)^2,k=0..6),n=1..35); # Muniru A Asiru, Jul 08 2018
  • Mathematica
    b = {}; a = 2; Do[k = Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a + Prime[n + 5]^a + Prime[n + 6]^a; AppendTo[b, k], {n, 1, 100}]; b
Total/@Partition[Prime[Range[40]]^2,7,1] (* Harvey P. Dale, Jan 01 2025 *)

Extensions

Edited by Michel Marcus, Jul 08 2018

A133557 Numbers k for which the sum of squares of five consecutive primes starting with prime(k) is prime (A133559).

Original entry on oeis.org

2, 3, 9, 10, 11, 16, 18, 25, 26, 28, 31, 33, 36, 42, 43, 46, 47, 54, 56, 58, 63, 68, 76, 87, 91, 93, 99, 101, 105, 106, 114, 127, 131, 145, 153, 159, 183, 186, 196, 201, 206, 229, 230, 232, 233, 238, 239, 241, 244, 245, 246, 248, 253, 256, 257, 264, 265, 266, 268
Offset: 1

Views

Author

Artur Jasinski, Sep 16 2007

Keywords

Comments

For sums of squares of two consecutive primes, only k=1 yields a prime.
For sums of squares of three consecutive primes A133529, it seems that only k=2 yields a prime (checked for all k < 1000000).
Sums of squares of four (and all even numbers of) consecutive primes are even numbers except at k=1.

Examples

			a(1)=2 because prime(2)^2 + prime(3)^2 + prime(4)^2 + prime(5)^2 + prime(6)^2 = 3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 373 is prime.

Crossrefs

Cf. A133538, A133559.

Programs

  • Mathematica
    b = {}; a = 2; Do[k = Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a; If[PrimeQ[k], AppendTo[b, n]], {n, 1, 100}]; b (* Artur Jasinski *)

Extensions

Name and example corrected by Jonathan Sondow, Nov 04 2015
Previous Showing 11-13 of 13 results.

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