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 1-2 of 2 results.

A033476 Squares of primes or products of pairs of consecutive primes.

Original entry on oeis.org

4, 6, 9, 15, 25, 35, 49, 77, 121, 143, 169, 221, 289, 323, 361, 437, 529, 667, 841, 899, 961, 1147, 1369, 1517, 1681, 1763, 1849, 2021, 2209, 2491, 2809, 3127, 3481, 3599, 3721, 4087, 4489, 4757, 5041, 5183, 5329, 5767, 6241, 6557, 6889, 7387, 7921, 8633
Offset: 0

Views

Author

Jeff Burch

Keywords

Crossrefs

Essentially the same as A057602.

A171645 Partial products of Product_{n=1..inf.} (p(n)/p(n-1)*p(n)/p(n-1)), = 2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7)*(11/7)*...; p = primes, A000040, a(1) = 2.

Original entry on oeis.org

2, 4, 8, 12, 18, 30, 50, 70, 98, 154, 242, 286, 338, 442, 578, 646, 722, 874, 1058, 1334, 1682, 1798, 1922, 2294, 2738
Offset: 1

Views

Author

Gary W. Adamson, Dec 13 2009

Keywords

Comments

Analogous formulas using A000041 terms = A171646; Fibonacci numbers, A006498; factorials, A010551.

Examples

			a(10) = 154 = 2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7).

Links

Crossrefs

Cf. A171646, A006498, A010551.

Programs

  • Mathematica
    FoldList[Times,Join[{2,2,2},Flatten[{#[[2]]/#[[1]],#[[2]]/#[[1]]}&/@Partition[Prime[Range[20]],2,1]]]] (* Harvey P. Dale, Oct 02 2024 *)

Formula

Partial products of Product_{n=1..inf.} (p(n)/p(n-1)*p(n)/p(n-1)), =
2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7)*(11/7)*...; p = primes,
A000040, a(1) = 2.
a(n)=2*A057602(n-1). [From R. J. Mathar, Dec 15 2009]
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.