cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A307252 Records in A319100.

Original entry on oeis.org

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

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Author

Jianing Song, Mar 31 2019

Keywords

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.

Examples

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

Crossrefs

Programs

  • 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
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