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%I #10 Oct 21 2019 11:37:07
%S 11,19,29,41,83,113,167,173,199,307,367,383,463,487,521,607,617,691,
%T 701,769,809,881,929,967,977,1423,1567,1579,1627,1753,2029,2063,2087,
%U 2207,2239,2251,2297,2341,2383,2393,2467,2477,2579,2657,2789,2833,3001,3533
%N 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.
%C Sum of reciprocals for the x+1 problem is around 0.318.
%C Sum of reciprocals for the 3x+1 problem is around 0.1116.
%C 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
%o (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) }
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Mar 26 2003
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