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

Author

Cino Hilliard, Mar 26 2003

Keywords

• easy
• nonn

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

Programs

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) }