A337376 - OEIS

A337376

Primorial deflation (numerator) of Doudna-tree.

1, 2, 3, 4, 5, 3, 9, 8, 7, 10, 5, 6, 25, 9, 27, 16, 11, 14, 21, 20, 7, 5, 15, 12, 49, 50, 25, 9, 125, 27, 81, 32, 13, 22, 33, 28, 55, 21, 63, 40, 11, 14, 7, 10, 35, 15, 45, 24, 121, 98, 147, 100, 49, 25, 25, 18, 343, 250, 125, 27, 625, 81, 243, 64, 17, 26, 39, 44, 65, 33, 99, 56, 91, 110, 55, 42, 275, 63, 189, 80, 13, 22

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Tree with both numerators (this sequence) and denominators (A337377) shown starts as:

1/1

3 / \ 4

- ................. ................. -

2 1

5 / \ 3 9 / \ 8

- ....... ....... - - ....... ....... -

3 1 4 1

/ \ / \ / \ / \

7 10 5 6 25 9 27 16

- -- - - -- - -- --

5 3 2 1 9 2 8 1

/ \ / \ / \ / \ / \ / \ / \ / \

11 14 21 20 7 5 15 12 49 50 25 9 125 27 81 32

-- -- -- -- - - -- -- -- -- -- - --- -- -- --

7 5 10 3 3 1 4 1 25 9 6 1 27 4 16 1

etc.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8191

Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Index entries for fraction trees

FORMULA

a(n) = A319626(A005940(1+n)).

a(n) = A005940(1+n) / A337375(n).

a(2*n) = A003961(a(n)).

If A007814(n+1) < A337821(n+1) then a(2*n+1) = a(n), otherwise a(2*n+1) = 2 * a(n).

If A337377(n) mod 2 = 0 then a(2*n+1) = a(n), otherwise a(2*n+1) = 2 * a(n).

A000265(a(2*n+1)) = A000265(a(n)).

A001222(a(2*n)) = A001222(A337377(2*n)) = A001222(a(n)).

A001222(a(2*n+1)) - A001222(A337377(2*n+1)) = 1 + A001222(a(n)) - A001222(A337377(n)).

MATHEMATICA

Array[#1/GCD[#1, #2] & @@ {#, Apply[Times, Map[If[#1 <= 2, 1, NextPrime[#1, -1]]^#2 & @@ # &, FactorInteger[#]]]} &@ Function[p, Times @@ Flatten@ Table[Prime[Count[Flatten[#], 0] + 1]^#[[1, 1]] &@ Take[p, -i], {i, Length[p]}]]@ Partition[Split[Join[IntegerDigits[# - 1, 2], {2}]], 2] &, 82] (* Michael De Vlieger, Aug 27 2020 *)

PROG

(PARI)

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};

A319626(n) = (n / gcd(n, A064989(n)));

A337376(n) = A319626(A005940(1+n));

CROSSREFS

A005940, A319626, A337375 are used in a formula defining this sequence.

Cf. A064989.

Cf. A337377 (denominators).

A000265, A001222, A003961, A007814, A337821 are used to express relationship between terms of this sequence.

Cf. also A329886, A346096.