The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A088643 Triangle read by rows: row n >= 1 is obtained as follows. Start with n, next term is always largest number m with 1 <= m < n which has not yet appeared in that row and such that m + previous term in the row is a prime. Stop when no further m can be found. 12
 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 2, 3, 4, 1, 6, 5, 2, 3, 4, 1, 7, 6, 5, 2, 3, 4, 1, 8, 5, 6, 7, 4, 3, 2, 1, 9, 8, 5, 6, 7, 4, 3, 2, 1, 10, 9, 8, 5, 6, 7, 4, 3, 2, 1, 11, 8, 9, 10, 7, 6, 5, 2, 3, 4, 1, 12, 11, 8, 9, 10, 7, 6, 5, 2, 3, 4, 1, 13, 10, 9, 8, 11, 12, 7, 6, 5, 2, 3, 4, 1, 14, 9, 10, 13, 6, 11, 12 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It is conjectured that row n is always a permutation of {1..n}. This has been verified for n <= 400000. Presumably many of the rows, when read from right to left, match the infinite sequence A055265. A255313(n,k) = T(n,k-1) + T(n,k), n > 0 and 1 <= k <= n. - Reinhard Zumkeller, Feb 22 2015 REFERENCES F. W. Roush and D. G. Rogers, A prime algorithm?, preprint, 1999. LINKS Reinhard Zumkeller, Rows n = 1..150 of triangle, flattened J. W. Roche, Letter regarding "M. J. Kenney and S. J. Bezuszka, Calendar problem 12, 1997", Mathematics Teacher, 91 (1998), 155. EXAMPLE For example, the 20th row is 20, 17, 14, 15, 16, 13, 18, 19, 12, 11, 8, 9, 10, 7, 6, 5, 2, 3, 4, 1. Triangle begins: 1 2 1 3 2 1 4 3 2 1 5 2 3 4 1 6 5 2 3 4 1 MATHEMATICA Clear[t]; t[n_, 1] := n; t[n_, k_] := t[n, k] = For[m = n-1, m >= 1, m--, If[ PrimeQ[m + t[n, k-1] ] && FreeQ[ Table[ t[n, j], {j, 1, k-1} ], m], Return[m] ] ]; Table[ t[n, k], {n, 1, 14}, {k, 1, n} ] // Flatten (* Jean-François Alcover, Apr 03 2013 *) PROG (Haskell) import Data.List (delete) a088643_tabl = map a088643_row [1..] a088643 n k = a088643_row n !! (k-1) a088643_row n = n : f n [n-1, n-2 .. 1] where    f u vs = g vs where      g []                            = []      g (x:xs) | a010051 (x + u) == 1 = x : f x (delete x vs)               | otherwise            = g xs -- Reinhard Zumkeller, Jan 05 2013 CROSSREFS A088631 and A088861 give second and third columns. Cf. A049476, A049477, A049478. Cf. A255313, A255316. Sequence in context: A233742 A194856 A278703 * A226620 A194877 A102482 Adjacent sequences:  A088640 A088641 A088642 * A088644 A088645 A088646 KEYWORD nonn,tabl,nice,easy AUTHOR N. J. A. Sloane, Nov 24 2003 EXTENSIONS More terms from David Wasserman, Aug 16 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 11:27 EDT 2020. Contains 334592 sequences. (Running on oeis4.)