A307252 Records in A319100.

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

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