login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A307252 Records in A319100. 1
1, 2, 6, 12, 24, 36, 48, 72, 144, 216, 288, 432, 864, 1296, 1728, 2592, 5184, 7776, 10368, 15552, 31104, 46656, 62208, 93312, 186624, 373248, 559872, 1119744, 2239488, 3359232, 4478976, 6718464, 13436928, 20155392, 26873856, 40310784, 80621568, 120932352 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All terms are of the form 6^u*2^j. Other than the term 48, k = 6^i*2^j is a term if and only if for all i', j' such that F(i',j') < F(i,j) we have 6^i'*2^j' < 6^i*2^j, where F(i,j) = Product_{s=1..i} (p_s)*Product_{t=1..j} (q_t), where p_1 = 7, p_2 = 9, p_s = A002476(s-1) for s >= 3; q_1 = 4, q_2 = 2, q_t = A007528(t-2) for t >= 3. Or equivalently: (a) for any u, v such that u <= i and 6^u < 2^v, Product_{s=i-u+1..i} (p_s) < Product_{t=j+1..j+v} (q_t); (b) for any u, v such that v <= j and 6^u > 2^v, Product_{s=i+1..i+u} (p_s) > Product_{t=j-v+1..j} (q_t). For example, 746496 = 6^6*2^4 is not a term because (q_3)*(q_4) = 5*11 > p_7 = 43.

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

A319100(168) = 48 which is larger than A319100(i) for i < 168, so 48 is a term.

PROG

(PARI) P(n) = if(!n, 1, if(n==1, 7, my(i=0, N=9); forprime(p=7, oo, if(p%3==1, i++; N*=p); if(i==n-1, return(N)))))

Q(n) = if(!n, 1, if(n==1, 4, my(i=0, N=4); forprime(p=2, oo, if(p%3==2, i++; N*=p); if(i==n-1, return(N)))))

v = []; for(i=0, 15, for(j=0, 15, if(P(i)*Q(j) < min(P(16), Q(16)), v=concat(v, [P(i)*Q(j)])))); v=vecsort(v);

u = []; for(i=1, #v, if(sum(j=1, i-1, A319100(v[j]) >= A319100(v[i]))==0, u=concat(u, [A319100(v[i])])));

vecsort(concat(u, [48])) \\ See A319100 for its program

CROSSREFS

Cf. A319100, A307251, A002476, A007528, A025610.

Sequence in context: A011778 A067718 A210594 * A306625 A262986 A307559

Adjacent sequences:  A307249 A307250 A307251 * A307253 A307254 A307255

KEYWORD

nonn

AUTHOR

Jianing Song, Mar 31 2019

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 22 21:25 EDT 2019. Contains 325227 sequences. (Running on oeis4.)