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A368085
Square array read by ascending antidiagonals: row n is the trajectory of P under the 'Px+1' map, where P = n-th prime.
5
2, 3, 5, 5, 10, 11, 7, 26, 5, 23, 11, 50, 13, 16, 47, 13, 122, 25, 66, 8, 95, 17, 170, 61, 5, 33, 4, 191, 19, 290, 85, 672, 1, 11, 2, 383, 23, 362, 145, 17, 336, 8, 56, 1, 767, 29, 530, 181, 29, 222, 168, 4, 28, 4, 1535, 31, 842, 265, 3440, 494, 111, 84, 2, 14, 2, 3071
OFFSET
1,1
COMMENTS
The 'Px+1 map' is defined as follows: if there exists p = smallest prime < P which divides x then x = x/p, otherwise x = P*x + 1.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..11325 (antidiagonals 1..150, flattened).
EXAMPLE
Array begins:
[ 1] 2, 5, 11, 23, 47, 95, 191, 383, 767, ... = A153893
[ 2] 3, 10, 5, 16, 8, 4, 2, 1, 4, ... = A033478
[ 3] 5, 26, 13, 66, 33, 11, 56, 28, 14, ... = A057688
[ 4] 7, 50, 25, 5, 1, 8, 4, 2, 1, ... = A368113
[ 5] 11, 122, 61, 672, 336, 168, 84, 42, 21, ... = A368114
[ 6] 13, 170, 85, 17, 222, 111, 37, 482, 241, ... = A057684
[ 7] 17, 290, 145, 29, 494, 247, 19, 324, 162, ... = A368115
[ 8] 19, 362, 181, 3440, 1720, 860, 430, 215, 43, ... = A057685
[ 9] 23, 530, 265, 53, 1220, 610, 305, 61, 1404, ... = A057686
[10] 29, 842, 421, 12210, 6105, 2035, 407, 37, 1074, ... = A057687
... | | |
A000040 | A066885 (from n = 2)
MATHEMATICA
Px1[p_, n_]:=Catch[For[i=1, i<PrimePi[p], i++, If[Divisible[n, Prime[i]], Throw[n/Prime[i]]]]; p*n+1];
A368085list[dmax_]:=With[{a=Reverse[Table[NestList[Px1[Prime[n], #]&, Prime[n], dmax-n], {n, dmax}]]}, Array[Diagonal[a, #]&, dmax, 1-dmax]];
A368085list[15] (* Generates 15 antidiagonals *)
CROSSREFS
Columns 1-3: A000040, A066872, A066885 (from n = 2).
Main diagonal gives A368159.
Sequence in context: A265562 A140312 A088887 * A265546 A066911 A326229
KEYWORD
nonn,tabl,easy
AUTHOR
Paolo Xausa, Dec 11 2023
STATUS
approved