A302774 - OEIS

%I #17 Jun 07 2018 22:06:56

%S 1,2,4,8,15,31,50,102,157,317,480,964,1451,2907,4366,8738,13113,26233,

%T 39356,78720,118087,236183,354282,708574,1062869

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

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

%C 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.

%o (PARI) prev=0; for(n=0,2^16,if(1==((p2=A061395(A303762(n)))-prev),print1(n,", ")); prev=p2);

%o (PARI)

%o allocatemem(2^30);

%o default(parisizemax,2^31);

%o up_to = (2^25)+2;

%o A053669(n) = forprime(p=2, , if (n % p, return(p))); \\ From A053669

%o A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

%o m_inverses = Map();

%o 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);

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

%K nonn

%O 1,2

%A _Antti Karttunen_, May 04 2018