A302774 a(n) is the position of the first term in A303762 that has prime(n) as one of its prime factors.

1, 2, 4, 8, 15, 31, 50, 102, 157, 317, 480, 964, 1451, 2907, 4366, 8738, 13113, 26233, 39356, 78720, 118087, 236183, 354282, 708574, 1062869

Offset

1,2

Comments

Equivalently, a(n) is the position of the first term k in A303769 for which 1+A000523(k) = n.

The first differences A303749 indicate how many terms were produced in each round of A303762 before the algorithm started outputting numbers with next larger prime as their greatest prime factor.

Links

Table of n, a(n) for n=1..25.

Prog

(PARI) prev=0; for(n=0, 2^16, if(1==((p2=A061395(A303762(n)))-prev), print1(n, ", ")); prev=p2);
(PARI)
allocatemem(2^30);
default(parisizemax, 2^31);
up_to = (2^25)+2;
A053669(n) = forprime(p=2, , if (n % p, return(p))); \\ From A053669
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
m_inverses = Map();
q2 = 0; prev=1; for(n=1, up_to, found_it = 0; fordiv(prev, d, if(!mapisdefined(m_inverses, (prev/d)), found_it = (prev/d); mapput(m_inverses, (prev/d), n); break)); if(!found_it, apu = prev; while(mapisdefined(m_inverses, try = prev*A053669(apu)), apu *= A053669(apu)); found_it = try; mapput(m_inverses, try, n)); if((q1=A061395(found_it)) != q2, write("b302774.txt", q1, " ", n-1); write("b302775.txt", q1, " ", found_it)); prev = found_it; q2 = q1);

Crossrefs

Cf. A061395, A302775, A303749, A303762, A303769.

Sequence in context: A251764 A191497 A052325 * A300520 A243082 A092603

Adjacent sequences: A302771 A302772 A302773 * A302775 A302776 A302777

Keyword

nonn

Author

Antti Karttunen, May 04 2018

Status

approved