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URL: https://oeis.org/A086762

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A086762
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.
1
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, 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, 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
OFFSET
2,1
COMMENTS
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?
PROG
(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); ) ) }
CROSSREFS
Sequence in context: A334456 A293343 A131626 * A296305 A349997 A076045
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Aug 02 2003
EXTENSIONS
Edited by Sam Alexander, Jan 05 2005
STATUS
approved