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A075348 Group the natural numbers such that the n-th 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 (list; table; graph; refs; listen; history; text; internal format)
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 !! (n-1) !! (k-1)

a075348_row n = a075348_tabl !! (n-1)

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

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Last modified June 19 23:01 EDT 2019. Contains 324222 sequences. (Running on oeis4.)