A080821 Primes in the accumulated tally of steps in the x+1 problem: Repeat until 1 is reached: if x is even divide by 2, otherwise add 1.

11, 19, 29, 41, 83, 113, 167, 173, 199, 307, 367, 383, 463, 487, 521, 607, 617, 691, 701, 769, 809, 881, 929, 967, 977, 1423, 1567, 1579, 1627, 1753, 2029, 2063, 2087, 2207, 2239, 2251, 2297, 2341, 2383, 2393, 2467, 2477, 2579, 2657, 2789, 2833, 3001, 3533

Offset

1,1

Comments

Sum of reciprocals for the x+1 problem is around 0.318.

Sum of reciprocals for the 3x+1 problem is around 0.1116.

The number of steps for the x+1 problem starting at n is A061313(n). The partial sums of A061313 are the sequence 0, 1, 4, 6, 11, 15, 19, 22, 29, 35, 41, ... Selecting the primes from these builds the current sequence. - R. J. Mathar, Feb 01 2008

Links

Table of n, a(n) for n=1..48.

Prog

(PARI) xpcount(n, p) = { ct=0; sr=0; for(x=1, n, p1 = x; while(p1>1, if(p1%2==0, p1/=2; ct++, p1 = p1*p+1; ct++) ); if(isprime(ct), print1(ct" "); sr+=1.0/ct) ); print(); print(sr) }

Crossrefs

Sequence in context: A034099 A034109 A155070 * A175275 A094517 A196669

Adjacent sequences: A080818 A080819 A080820 * A080822 A080823 A080824

Keyword

easy,nonn

Author

Cino Hilliard, Mar 26 2003

Status

approved