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

Author

Antti Karttunen, May 04 2018

Keywords

• nonn

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.

Crossrefs

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

Programs

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);