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

%I A302774 #17 Jun 07 2018 22:06:56
%S A302774 1,2,4,8,15,31,50,102,157,317,480,964,1451,2907,4366,8738,13113,26233,
%T A302774 39356,78720,118087,236183,354282,708574,1062869
%N A302774 a(n) is the position of the first term in A303762 that has prime(n) as one of its prime factors.
%C A302774 Equivalently, a(n) is the position of the first term k in A303769 for which 1+A000523(k) = n.
%C A302774 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 A302774 (PARI) prev=0; for(n=0,2^16,if(1==((p2=A061395(A303762(n)))-prev),print1(n,", ")); prev=p2);
%o A302774 (PARI)
%o A302774 allocatemem(2^30);
%o A302774 default(parisizemax,2^31);
%o A302774 up_to = (2^25)+2;
%o A302774 A053669(n) = forprime(p=2, , if (n % p, return(p))); \\ From A053669
%o A302774 A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
%o A302774 m_inverses = Map();
%o A302774 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 A302774 Cf. A061395, A302775, A303749, A303762, A303769.
%K A302774 nonn
%O A302774 1,2
%A A302774 _Antti Karttunen_, May 04 2018