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.

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?

Links

Table of n, a(n) for n=2..90.

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

Cf. A086763, A000265.

Sequence in context: A334456 A293343 A131626 * A296305 A349997 A076045

Adjacent sequences: A086759 A086760 A086761 * A086763 A086764 A086765

Keyword

easy,nonn

Author

Cino Hilliard, Aug 02 2003

Extensions

Edited by Sam Alexander, Jan 05 2005

Status

approved