A082010 -id:A082010 - cp's OEIS frontend

A152199 Trajectory of 7 under the map m -> A082010(m).

7, 12, 6, 3, 5, 9, 15, 25, 41, 66, 33, 53, 85, 137, 220, 110, 55, 89, 143, 229, 367, 588, 294, 147, 236, 118, 59, 95, 153, 245, 393, 629, 1007, 1612, 806, 403, 645, 1033, 1653, 2645, 4233, 6773, 10837, 17340, 8670, 4335, 6937, 11100, 5550, 2775, 4441, 7106

Offset: 1

N. J. A. Sloane, Oct 06 2009, suggested by a posting to the Sequence Fans Mailing List by Yasutoshi Kohmoto, Sep 30 2009

nonn

First differences: 5, -6, -3, 2, 4, 6, 10, 16, 25, -33, 20, 32, 52, 83, -110, -55, 34, 54, 86, 138, 221, -294, -147, 89, -118, -59, 36, 58, 92, 148, 236, 378, 605, -806, -403, 242, 388, 620, 992, 1588, 2540, 4064, 6503, -8670, -4335, 2602, 4163, -5550, -2775, 1666, 2665, -3553, 2132, 3412, 5459, -7278, -3639, 2184, 3494, 5591, -7454, -3727, 2237, -2982, -1491, 895, -1193, 716, 1146, 1834, 2934, 4694, 7511, -10014, -5007, 3005, -4006, -2003, 1202, 1924, 3078, 4925, -6566, -3283, 1970, 3152, 5044, 8070, 12912, 20659, -27545, 16528, 26444, 42311, -56414, -28207, 16925, -22566, -11283, 6770. [Zak Seidov, Oct 07 2009]

Robert Israel, Table of n, a(n) for n = 1..10000

A082010 := proc(n) if type(n,'even') then n/2; else 1+floor(8*n/5) ; fi; end: A152199 := proc(n) option remember; if n = 1 then 7; else A082010(procname(n-1)) ; fi; end: seq(A152199(n),n=1..100) ; # R. J. Mathar, Oct 07 2009

NestList[If[EvenQ[ # ], #/2, Floor[8*#/5] + 1] &, 7, 100] (* Zak Seidov, Oct 07 2009 *)

More terms from R. J. Mathar and Zak Seidov, Oct 07 2009

A082006 In the following square array numbers (not occurring earlier) are entered like this: a(1, 1), a(1, 2), a(2, 1), a(3, 1), a(2, 2), a(1, 3), a(1, 4), a(2, 3), a(3, 2), a(4, 1), a(5, 1), a(4, 2), ... such that every entry is coprime to the members of the row and column it belongs, with the condition that the n-th diagonal sum is a multiple of n. 1 2 7 9 31 25... 4 5 11 23 27... 3 13 8... 19 21... 17 ... ... Sequence contains numbers as they are entered.

Original entry on oeis.org

1, 2, 4, 3, 5, 7, 9, 11, 13, 19, 17, 21, 8, 23, 31, 25, 27, 29, 37, 41

Offset: 1

Amarnath Murthy, Apr 05 2003

Next term T(6,1) =a(21)> 500000, a(21) is odd. The sum of the first diagonal is 1 (a multiple of 1). The sum of the second diagonal is T(1,2)+T(2,1)=2+4=6 (a multiple of 2). The sum of the 3rd diagonal is T(1,3)+T(2,2)+T(3,1)=7+5+3=15 (a multiple of 3). The sum of the 4th diagonal is T(1,4)+T(2,3)+T(3,2)+T(4,1)=9+11+13+19=52 (a multiple of 4). The members of the first row (1,2,7,9,31,25,..) are mutually coprime. The members of the 2nd row (4,5,11,23,27,..) are mutually coprime. The members of the first column (1,4,3,19,17,..) are mutually coprime. The members of the 2nd column (2,5,13,21,..) are mutually coprime. The a(n) transverses the table in meandering fashion: first diagonal up, 2nd diagonal down, 3rd diagonal up, 4th down etc. - R. J. Mathar, May 06 2006
From Alois P. Heinz, Oct 06 2009: (Start)
T(6,1) is undefined, so there are no further terms.
For T(6,1) would be == 3 (mod 6) w.r.t. antidiagonal 6, (T(6,1)+159=6k) and it would be == 1 or == 5 (mod 6) w.r.t. column 1 (coprime to 3 & 4) which is impossible, unless backtracking is allowed and earlier elements are altered. But that is not intended by the author, because "sequence contains numbers as they are entered", and it would not make a valid definition at all. (End)

			Table is
1 2 7 9 31 25
4 5 11 23 27
3 13 8 29
19 21 37
17 41
?

Cf. A082002, A082003, A082004, A082005, A082007, A082008, A082009, A082010.

More terms from R. J. Mathar, May 06 2006

cp's OEIS Frontend

A152199 Trajectory of 7 under the map m -> A082010(m).

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