

A075348


Group the natural numbers such that the nth group contains n terms and the group sum is the smallest possible prime: (2), (1, 4), (3, 5, 9), (6, 7, 8, 10), (11, 12, 13, 14, 17), (15, 16, 18, 19, 20, 21), ... yield the rows of this table.


6



2, 1, 4, 3, 5, 9, 6, 7, 8, 10, 11, 12, 13, 14, 17, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 32, 28, 29, 30, 31, 33, 34, 35, 37, 36, 38, 39, 40, 41, 42, 43, 44, 50, 45, 46, 47, 48, 49, 51, 52, 53, 54, 58, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 71, 66, 67, 68, 69, 70, 72
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OFFSET

1,1


COMMENTS

Row sums (the primes) are in A075345. In case of several possibilities to write the given prime, e.g. A075345(3) = 3+5+9 = 3+6+8, the lexicographically smallest is to be chosen, here (3,5,9) rather than (3,6,8).  M. F. Hasler, Sep 26 2015
The flattened triangle is a permutation of the positive integers with inverse = A262663 and fixed points A262665.


LINKS

Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened
Index entries for sequences that are permutations of the natural numbers


FORMULA

T(n,1)=A075346(n); T(n,n)=A075347(n); A075344(n)=sum(T(n,k): k=1..n).  Reinhard Zumkeller, Sep 26 2015


EXAMPLE

Triangle starts:
2;
1,4;
3,5,9;
6,7,8,10;
...


PROG

(Haskell)
import Data.List ((\\))
a075348 n k = a075348_tabl !! (n1) !! (k1)
a075348_row n = a075348_tabl !! (n1)
a075348_tabl = f 0 [1..] where
f x zs = (us ++ [y]) : f (x + 1) (zs \\ (y : us)) where
y = g vs
g (w:ws) = if a010051' (sum us + w) == 1 then w else g ws
(us, vs) = splitAt x zs
a075348_list = concat a075348_tabl
 Reinhard Zumkeller, Sep 26 2015


CROSSREFS

Cf. A075345, A075346, A075347.
Cf. A262663 (inverse), A262665 (fixed points).
Sequence in context: A324755 A259019 A262663 * A326062 A055631 A234586
Adjacent sequences: A075345 A075346 A075347 * A075349 A075350 A075351


KEYWORD

nonn,tabl


AUTHOR

Amarnath Murthy, Sep 19 2002


EXTENSIONS

Extended by Ray Chandler, Apr 09 2014
Name changed by M. F. Hasler, Sep 26 2015


STATUS

approved



