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
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
-
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 *)
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
-
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 *)
More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 05 2004
A090907
Ratio of products of successive rows of the irregular triangle defined in A090905.
Original entry on oeis.org
2, 6, 140, 1287, 2139552000, 2949442889323392, 322686644032484531917367528014184448000000
Offset: 1
a(1)=(2!/1!)*(0!/1!)
a(2)=(4!/2!)*(1!/2!)
a(3)=(8!/4!)*(2!/4!)
a(4)=(14!/8!)*(4!/8!)
a(5)=(26!/14!)*(8!/14!)
a(6)=(46!/26!)*(14!/26!)
For n>=6 we have a(n)= ((2*A006992(n))!/(2*A006992(n-1))!)*((2*A006992(n-2))!/(2*A006992(n-1))!), verified for 4<n<21
Edited by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 05 2004
A093911
Left side of irregular triangle of natural numbers in which the n-th row has at least n terms and every row product is a multiple of the previous.
Original entry on oeis.org
1, 2, 4, 7, 11, 17, 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
The first 5 groups are (1), (2,3), (4,5,6), (7,8,9,10),
(11,12,13,14,15,16). The 5th group ends with 16 because
11*12*13*14*15*16 is divisible by 7*8*9*10, but 11*12*13*14*15 is not.
-
a = {{1, 1}, {2, 2}}; Do[k = Last@ a[[i]]; While[! Divisible[Pochhammer[Total@ a[[i]], k], Pochhammer @@ a[[i]]], k++]; AppendTo[a, {Total@ a[[i]], k}], {i, 2, 16}]; Last /@ a (* Michael De Vlieger, Dec 15 2016 *)
A381901
Partition the natural numbers by letting a(1)=1 (denoting the set {1}) and for n>1 define a(n) to be the least integer such that the product of the set of integers {a(n-1)+1,...,a(n)} is an integer multiple of the previous partition's product.
Original entry on oeis.org
1, 2, 4, 8, 14, 26, 46, 86, 166, 326, 634, 1262, 2518, 5006, 10006, 19946, 39874, 79738, 159398, 318778, 637502, 1274998, 2549978, 5099902, 10199786, 20399534, 40799062, 81598082, 163196134, 326392258, 652784498, 1305568942, 2611137838, 5222275634, 10444551254
Offset: 1
The first few corresponding partitions are {1}, {2}, {3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12, 13, 14}.
Appears to agree with
A113117 starting at the 5th term and with
A113118 starting at the 6th term.
Showing 1-5 of 5 results.
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