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%I #8 Feb 11 2021 14:22:21
%S 1,1,1,1,2,2,1,1,1,1,1,1,2,3,2,1,1,1,1,2,4,3,3,3,1,1,1,1,2,3,2,1,2,1,
%T 2,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,3,1,4,1,3,3,1,4,1,1,2,1,6,2,1,1,2,
%U 2,2,3,4,2,3,2,1,1,1,2,1,1,1,4,1,2,1,1,1,2,2,2,3,3,4,1,1,2,1,1,1,4,1,5,3,1
%N Runlengths of A341346.
%C Records 1, 2, 3, 4, 7, 8, 11, 12, 14, 15, 19, 23, ..., occur at n = 1, 5, 14, 21, 51, 162, 319, 851, 1543, 6568, 91616, 608928, ...
%H Antti Karttunen, <a href="/A341348/b341348.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%e A341346 begins as 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, ...,
%e thus this sequence begins as 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, ...
%o (PARI)
%o up_to = 65537;
%o A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A341346(n) = (((A003961(n+n-1)+1)/2)%3);
%o A341348lista(up_to) = { my(v=vector(up_to), r=1, n=0, i=2, pb=1, b); while(n<up_to, b = A341346(i); if(b==pb, r++, n++; v[n] = r; r = 1; pb = b); i++); (v); };
%o v341348 = A341348lista(up_to);
%o A341348(n) = v341348[n];
%Y Cf. A003961, A048673, A341346.
%K nonn
%O 1,5
%A _Antti Karttunen_, Feb 10 2021
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