A353265 Partial sums of A208981.

0, 0, 3, 3, 4, 8, 20, 20, 35, 37, 47, 52, 57, 70, 83, 83, 91, 107, 123, 126, 127, 138, 149, 155, 174, 180, 287, 301, 315, 329, 431, 431, 453, 462, 471, 488, 505, 522, 552, 556, 661, 663, 688, 700, 712, 724, 824, 831, 851, 871, 891, 898, 905, 1013, 1121, 1136, 1164, 1179, 1207, 1222, 1237, 1340, 1443, 1443

Offset: 1

Author

Omar E. Pol, Apr 09 2022

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A208981, A347270 (gives all 3x+1 sequences).

Cf. A006370, A006877, A014682, A347272, A347519, A352907, A352908, A352939.

Programs

Mathematica

Accumulate @ Table[-1 + Length @ NestWhileList[If[OddQ[#], 3*# + 1, #/2] &, n, ! IntegerQ @ Log[2, #] &], {n, 1, 64}] (* Amiram Eldar, Apr 09 2022 *)

PARI

ispow2(n)=n>>=valuation(n, 2); n==1;
f(n) = my(s); while(!ispow2(n), n=if(n%2, 3*n+1, n/2); s++); s; \\ A208981
a(n) = sum(i=1, n, f(i)); \\ Michel Marcus, Apr 13 2022