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A090905 Left side of irregular triangle of natural numbers in which every row product is a multiple of the previous. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

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)...

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 *)

CROSSREFS

Cf. A090904, A090906, A090907.

Sequence in context: A190138 A273905 A022858 * A065956 A178738 A060013

Adjacent sequences:  A090902 A090903 A090904 * A090906 A090907 A090908

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Dec 13 2003

EXTENSIONS

More terms from David Wasserman, Feb 10 2006

STATUS

approved

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Last modified January 23 15:22 EST 2017. Contains 281201 sequences.