cp's OEIS Frontend

A358166 a(1) = 13; for n > 1, if a(n-1) is even, then a(n) = a(n-1)/2; otherwise, a(n) = a(n-1) + prime(a(n-1)).

%I A358166 #30 Dec 06 2022 07:59:13
%S A358166 13,54,27,130,65,378,189,1318,659,5592,2796,1398,699,5972,2986,1493,
%T A358166 13996,6998,3499,36102,18051,218932,109466,54733,730334,365167,
%U A358166 5622764,2811382,1405691,23685544,11842772,5921386,2960693,52246474,26123237,521463688,260731844,130365922,65182961,1364229390
%N A358166 a(1) = 13; for n > 1, if a(n-1) is even, then a(n) = a(n-1)/2; otherwise, a(n) = a(n-1) + prime(a(n-1)).
%C A358166 Does this sequence become cyclic? All the sequences defined the same as this one but with 1 <= a(1) <= 12 are known to become cyclic.
%C A358166 a(81) = 1977693361846020549, so calculating a(82) will require calculating the 1977693361846020549th prime.
%e A358166 a(1) = 13 is odd, so a(2) = 13 + prime(13) = 13 + 41 = 54.
%e A358166 a(2) = 54 is even, so a(3) = a(2)/2 = 54/2 = 27.
%e A358166 a(3) = 27 is odd, so a(4) = 27 + prime(27) = 27 + 103 = 130, etc.
%t A358166 NestList[If[EvenQ[#], #/2, # + Prime[#]] &, 13, 40]
%o A358166 (PARI) lista(nn) = my(va = vector(nn)); va[1] = 13; for (n=2, nn, if (va[n-1] % 2, va[n] = va[n-1] + prime(va[n-1]), va[n] = va[n-1]/2);); va; \\ _Michel Marcus_, Nov 12 2022
%Y A358166 Cf. A293981, A350877, A014688.
%K A358166 nonn,look,hard
%O A358166 1,1
%A A358166 _Sander G. Huisman_, Nov 01 2022