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, 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

Offset

1,1

Comments

Row sums (the primes) are in A075345. In case there is more than one way 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_{k=1..n} T(n,k). - Reinhard Zumkeller, Sep 26 2015

Example

Triangle starts:
   2;
   1,  4;
   3,  5,  9;
   6,  7,  8, 10;
  11, 12, 13, 14, 17;
  15, 16, 18, 19, 20, 21;
  ...

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