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%I #6 Oct 09 2013 14:20:13
%S 7,11,17,13,5,1,5,1,1,1,3,5,1,11,17,13,5,1,1,5,1,5,1,17,13,5,1,3,5,1,
%T 5,1,7,11,17,13,5,1,1,1,13,5,1,9,5,1,29,11,17,13,5,1,5,1,11,17,13,5,1,
%U 11,17,13,5,1,35,9,5,1,3,5,1,13,5,1,13,5,1,7,11,17,13,5,1,7,11,17,13,5,1
%N A piecewise recurrence relation with a(2)=7 and for n>=2: if a(n) is prime, not 31, a(n+1) = A000265(3*a(n)+1); if a(n) is odd composite, not 1, a(n+1) = A000265(a(n)+1); if a(n) is even, a(n+1) = A000265(a(n)); if a(n) is 1 or 31, find the number S(n) of occurrences of 1 and 31 among a(2),a(3),...,a(n) and compute a(n+1) by the above rules as if a(n) were 2+S(n), unless 2+S(n)=31, in which case a(n+1)=47.
%C Note that if we treated 31 like the other primes, we would enter the infinite loop 31, 47, 71, 107, 161, 81, 41, 31. Are there any remaining infinite loops?
%o (PARI) pxp1(m) = { for(x=2,m, n=x; while(n > 1, if(isprime(n),n=n*3+1,if(n%2<>0,n++)); while(n%2==0,n/=2); print1(n","); if(n==1 || n==31,break); ) ) }
%Y Cf. A086763, A000265.
%K easy,nonn
%O 2,1
%A _Cino Hilliard_, Aug 02 2003
%E Edited by _Sam Alexander_, Jan 05 2005
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