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)).

13, 54, 27, 130, 65, 378, 189, 1318, 659, 5592, 2796, 1398, 699, 5972, 2986, 1493, 13996, 6998, 3499, 36102, 18051, 218932, 109466, 54733, 730334, 365167, 5622764, 2811382, 1405691, 23685544, 11842772, 5921386, 2960693, 52246474, 26123237, 521463688, 260731844, 130365922, 65182961, 1364229390

Offset: 1

Author

Sander G. Huisman, Nov 01 2022

Keywords

• nonn
• look
• hard

Comments

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.

a(81) = 1977693361846020549, so calculating a(82) will require calculating the 1977693361846020549th prime.

Examples

			a(1) = 13 is odd, so a(2) = 13 + prime(13) = 13 + 41 = 54.
a(2) = 54 is even, so a(3) = a(2)/2 = 54/2 = 27.
a(3) = 27 is odd, so a(4) = 27 + prime(27) = 27 + 103 = 130, etc.
		

Crossrefs

Cf. A293981, A350877, A014688.

Programs

Mathematica

NestList[If[EvenQ[#], #/2, # + Prime[#]] &, 13, 40]

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