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.

A090904 Row products of the irregular triangle defined in A090905.

Original entry on oeis.org

1, 2, 12, 1680, 2162160, 4626053752320000, 13644281345408020027550269440000, 4402827357584746886229433170489943024971625310770489684257669120000000000
Offset: 1

Views

Author

Amarnath Murthy, Dec 13 2003

Keywords

Comments

Conjecture: For n > 4 the last term of the n-th group is 2p where p is the largest prime in the (n-1)th group. And these are the Bertrand primes.

Examples

			a(3) = 1680 because a(1) is the product of 1 successive number starting with 1 = 1, a(2) is the product of 1 successive number (2) = 2, a(3) is the product of 2 successive numbers (3,4) = 12, finally a(4) is the product of 4 successive numbers (5,6,7,8) = 1680. All the products have the property that a(n) = 0 (mod a(n - 1)). Thus a(4) = 1680. - _Michael De Vlieger_, Dec 22 2016
		

Crossrefs

Programs

  • Mathematica
    a = {{1, 1}}; Do[k = Last@ a[[i - 1]]; While[! Divisible[Pochhammer[Total@ a[[i - 1]], k], Pochhammer @@ a[[i - 1]]], k++]; AppendTo[a, {Total@ a[[i - 1]], k}], {i, 2, 8}]; Pochhammer @@ # & /@ a (* Michael De Vlieger, Dec 15 2016 *)

Extensions

More terms from David Wasserman, Feb 10 2006

A090905 Left side of irregular triangle of natural numbers in which every row product is a multiple of the previous.

Original entry on oeis.org

1, 2, 3, 5, 9, 15, 27, 47, 87, 167, 327, 635, 1263, 2519, 5007, 10007, 19947, 39875, 79739, 159399, 318779, 637503, 1274999, 2549979, 5099903, 10199787, 20399535, 40799063, 81598083, 163196135, 326392259, 652784499, 1305568943, 2611137839
Offset: 1

Views

Author

Amarnath Murthy, Dec 13 2003

Keywords

Comments

Conjecture: For n > 4 the last term of the n-th group is 2p where p is the largest prime in the (n-1)th group. And these are the Bertrand primes.

Examples

			The triangle goes as follows:
(1)
(2),
(3,4),
(5,6,7,8),
(9,10,11,12,13,14),
(15,16,17,18,19,20,21,22,23,24,25,26)...
		

Crossrefs

Programs

  • Mathematica
    a = {{1, 1}}; Do[k = Last@ a[[i - 1]]; While[!Divisible[Pochhammer[Total@ a[[i - 1]], k], Pochhammer @@ a[[i - 1]]], k++]; AppendTo[a, {Total@a[[i - 1]], k}], {i, 2, 17}]; a (* Michael De Vlieger, Dec 15 2016 *)

Extensions

More terms from David Wasserman, Feb 10 2006

A090906 Row lengths of the irregular triangle defined in A090905.

Original entry on oeis.org

1, 1, 2, 4, 6, 12, 20, 40, 80, 160, 308, 628, 1256, 2488, 5000, 9940, 19928, 39864, 79660, 159380, 318724, 637496, 1274980, 2549924, 5099884, 10199748, 20399528, 40799020, 81598052, 163196124, 326392240, 652784444, 1305568896, 2611137796
Offset: 1

Views

Author

Amarnath Murthy, Dec 13 2003

Keywords

Comments

Conjecture: For n > 4 the last term of the n-th group is 2p where p is the largest prime in the (n-1)th group. And these are the Bertrand primes.

Crossrefs

Programs

  • Mathematica
    a = {{1, 1}}; Do[k = Last@ a[[i - 1]]; While[! Divisible[Pochhammer[Total@ a[[i - 1]], k], Pochhammer @@ a[[i - 1]]], k++]; AppendTo[a, {Total@a[[i - 1]], k}], {i, 2, 17}]; Last /@ a (* Michael De Vlieger, Dec 15 2016 *)

Formula

For n>4 a(n)= 2*(A006992(n)-A006992(n-1)) - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 05 2004

Extensions

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 05 2004
More terms from David Wasserman, Feb 10 2006

A093913 Ratio of products of successive rows of irregular triangle defined in A093911.

Original entry on oeis.org

6, 20, 42, 1144, 3343050, 707866293437614080, 322686644032484531917367528014184448000000
Offset: 1

Views

Author

Amarnath Murthy, Apr 24 2004

Keywords

Comments

Next term has 95 digits.

Crossrefs

Formula

a(n) = A093910(n+1)/A093910(n).

Extensions

Edited and extended by David Wasserman, Mar 27 2006
Showing 1-4 of 4 results.