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.

User: Alan Griffiths

Alan Griffiths's wiki page.

Alan Griffiths has authored 2 sequences.

A211133 Odd sides belonging to multiple primitive Euler bricks.

Original entry on oeis.org

1155, 4599, 5643, 8415, 9405, 10395, 10725, 66495, 200385, 1100385, 1769229, 2518725, 2673585, 2807805, 4150575, 4362115, 8191161, 8954495, 11534489, 12645009, 13435565, 19875933, 25560909, 31122325, 45285075, 45930885, 55257111, 62379225, 75081435, 93205889
Offset: 1

Author

Alan Griffiths, May 11 2012

Keywords

Comments

Primitive Euler bricks are defined by (a, b, c) where a^2+b^2=u^2, b^2+c^2=v^2, a^2+c^2=w^2, gcd(a, b, c) = 1, and all values are integers, thus defining a cuboid with integer edges and face diagonals.
At most one of a, b, and c must be odd. This list shows those odd values which belong to more than one valid (a, b, c) set.

A133155 Numbers formed by setting bits representing odd primes, where bit_no = (prime - 1)/2. Setting bit number b is the same as OR-ing with 2^b (i.e., bit numbers start at zero).

Original entry on oeis.org

2, 6, 14, 46, 110, 366, 878, 2926, 19310, 52078, 314222, 1362798, 3459950, 11848558, 78957422, 615828334, 1689570158, 10279504750, 44639243118, 113358719854, 663114533742, 2862137789294, 20454323833710, 301929300544366, 1427829207386990, 3679629021072238
Offset: 1

Author

Alan Griffiths, Oct 08 2007

Keywords

Examples

			a(3) = 14 because 3, 5 and 7 are odd primes so therefore bits 1, 2 and 3 are set and bit zero is not. 1110_2 = 14.
		

Crossrefs

Partial sums of A061285.

Programs

  • Python
    import gmpy
    a = gmpy.mpz(0)
    i = 0
    for p in range(3,100,2):
        if gmpy.is_prime(p):
            a = gmpy.setbit(a,(p-1)/2)
            i += 1
            print(i,a)

Formula

a(n) = setbit(a(n-1),(p-1)/2) where p is the n-th odd prime.