The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Chris Boyd (See also Chris Boyd's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A323185

Denominators of rationals whose continued fraction representations show the prime factors of n (for n > 1) in nondecreasing order.
(history; published version)

#7 by Chris Boyd at Mon Jan 07 03:41:29 EST 2019

STATUS

editing

proposed

A323184

Numerators of rationals whose continued fraction representations show the prime factors of n (for n>1) in nondecreasing order.
(history; published version)

#8 by Chris Boyd at Mon Jan 07 03:41:08 EST 2019

STATUS

editing

proposed

A323185

Denominators of rationals whose continued fraction representations show the prime factors of n (for n > 1) in nondecreasing order.
(history; published version)

#6 by Chris Boyd at Mon Jan 07 03:35:15 EST 2019

NAME

Denominators of rationals whose continued fraction representations show the prime factors of n+ (for n>1 ) in nondecreasing order.

OFFSET

1,2,1

COMMENTS

a(n) is the denominator of the generating rational of n+1 (see comments and numerators in A323184).

If n+1 is prime, a(n) is n+1.

LINKS

Chris Boyd, <a href="/A323185/b323185.txt">Table of n, a(n) for n = 1..10000</a>

Chris Boyd, Table of n, a(n) for n = 1..10000

EXAMPLE

a(2728) = 37 because 15/37 = [0; 2, 2, 7] and 2*2*7 = 28.

a(2829) = 29 because 1/29 = [0; 29] = 29.

PROG

A323185(n)={vectorise_factors(n+1); contfracpnqn(v)[2, 1]; }

for(k=1, 2, 75, print1(A323185(k)", ")) \\ _Chris Boyd_, Jan 06 2019

STATUS

proposed

editing

Discussion

Mon Jan 07

03:41

Chris Boyd: Changes mirror those made for A323184.

A323184

Numerators of rationals whose continued fraction representations show the prime factors of n (for n>1) in nondecreasing order.
(history; published version)

#7 by Chris Boyd at Mon Jan 07 03:30:56 EST 2019

NAME

Numerators of rationals whose continued fraction representations show the prime factors of n+ (for n>1 ) in nondecreasing order.

OFFSET

1,2,3

COMMENTS

a(n) is the numerator of the generating rational of n+1.

Iff n+1 is prime, a(n) is 1.

LINKS

Chris Boyd, <a href="/A323184/b323184.txt">Table of n, a(n) for n = 1..10000</a>

Chris Boyd, Table of n, a(n) for n = 1..10000

EXAMPLE

a(2728) = 15 because 15/37 = [0; 2, 2, 7] and 2*2*7 = 28.

a(2829) = 1 because 1/29 = [0; 29] = 29.

PROG

A323184(n)={vectorise_factors(n+1); contfracpnqn(v)[1, 1]; }

for(k=1, 2, 75, print1(A323184(k)", ")) \\ _Chris Boyd_, Jan 06 2019

STATUS

proposed

editing

Discussion

Mon Jan 07

03:32

Chris Boyd: Thanks, I have made all your suggested changes including  new offset.

A323185

Denominators of rationals whose continued fraction representations show the prime factors of n (for n > 1) in nondecreasing order.
(history; published version)

#5 by Chris Boyd at Sun Jan 06 12:06:47 EST 2019

STATUS

editing

proposed

Discussion

Sun Jan 06

12:10

Michel Marcus: no need to sign program, you are the author of sequence;

please next time, do not add a bfile bfore sequence is approved : see last bullet of https://oeis.org/wiki/Style_Sheet#Links

A323184

Numerators of rationals whose continued fraction representations show the prime factors of n (for n>1) in nondecreasing order.
(history; published version)

#6 by Chris Boyd at Sun Jan 06 12:06:33 EST 2019

STATUS

editing

proposed

Discussion

Sun Jan 06

12:08

Michel Marcus: no need to sign program, you are the author of sequence

12:09

Michel Marcus: please next time, do not add a bfile bfore sequence is approved : see last bullet of https://oeis.org/wiki/Style_Sheet#Links

12:11

Michel Marcus: the indexing is a bit weird: a(n) corresponds to n+1; why not have offset 2 and a(n) corresponding to n

12:12

Michel Marcus: I guess this line can go ? Chris Boyd, Table of n, a(n) for n = 1..10000

A323185

Denominators of rationals whose continued fraction representations show the prime factors of n (for n > 1) in nondecreasing order.
(history; published version)

#4 by Chris Boyd at Sun Jan 06 12:00:38 EST 2019

NAME

Denominators of rationals whose continued fraction representation shows representations show the prime factors of n+1 in nondecreasing order.

A323184

Numerators of rationals whose continued fraction representations show the prime factors of n (for n>1) in nondecreasing order.
(history; published version)

#5 by Chris Boyd at Sun Jan 06 11:58:45 EST 2019

NAME

Numerators of rationals whose continued fraction representation shows representations show the prime factors of n+1 in nondecreasing order.

COMMENTS

There is a unique positive finite continued fraction associated with N whose coefficients in the standard abbreviated notation (except for the first coefficient, which is arbitrarily set to zero) map 1-to-1 to the elements of the tuple, from which the corresponding generating rational can be calculated (e.g. 60 = -> [0; 2, 2, 3, 5] = 37/90).

...

A323185

Denominators of rationals whose continued fraction representations show the prime factors of n (for n > 1) in nondecreasing order.
(history; published version)

#3 by Chris Boyd at Sun Jan 06 11:50:39 EST 2019

NAME

Denominators of rationals whose continued fraction representation shows the prime factors of n+1 in non-decreasing nondecreasing order.

LINKS

Chris Boyd, <a href="/A323185/b323185.txt">Table of n, a(n) for n = 1..10000</a>

#2 by Chris Boyd at Sun Jan 06 11:46:46 EST 2019

NAME

allocated for Chris BoydDenominators of rationals whose continued fraction representation shows the prime factors of n+1 in non-decreasing order.

DATA

2, 3, 5, 5, 7, 7, 12, 10, 11, 11, 17, 13, 15, 16, 29, 17, 23, 19, 27, 22, 23, 23, 41, 26, 27, 33, 37, 29, 37, 31, 70, 34, 35, 36, 56, 37, 39, 40, 65, 41, 51, 43, 57, 53, 47, 47, 99, 50, 57, 52, 67, 53, 76, 56, 89, 58, 59, 59, 90, 61, 63, 73, 169, 66, 79, 67, 87

OFFSET

1,1

COMMENTS

a(n) is the denominator of the generating rational of n+1 (see comments and numerators in A323184).

If n+1 is prime, a(n) is n+1.

LINKS

Chris Boyd, Table of n, a(n) for n = 1..10000

EXAMPLE

a(27) = 37 because 15/37 = [0; 2, 2, 7] and 2*2*7 = 28.

a(28) = 29 because 1/29 = [0; 29] = 29.

PROG

(PARI) vectorise_factors(m)={v=[0]; F=factor(m); for(i=1, matsize(F)[1], for(j=1, F[i, 2], v=concat(v, F[i, 1]))); }

A323185(n)={vectorise_factors(n+1); contfracpnqn(v)[2, 1]; }

for(k=1, 75, print1(A323185(k)", ")) \\ Chris Boyd, Jan 06 2019

CROSSREFS

Cf. A323184.

KEYWORD

allocated

nonn,frac

AUTHOR

Chris Boyd, Jan 06 2019

STATUS

approved

editing