A225748 -id:A225748 - cp's OEIS frontend

A274243 Numbers n for which the sum of the odd numbers in the Collatz (3x+1) iteration of n is prime.

11, 13, 22, 26, 44, 52, 53, 67, 88, 104, 105, 106, 113, 121, 131, 134, 165, 176, 187, 208, 210, 211, 212, 226, 227, 231, 242, 243, 257, 261, 262, 268, 273, 289, 291, 293, 325, 329, 330, 352, 373, 374, 416, 419, 420, 422, 424, 431, 447, 452, 454, 461, 462, 473

Offset: 1

Michel Lagneau, Jul 01 2016

nonn

The corresponding primes are 47, 19, 47, 19, 47, 19, 59, 263, 47, 19, 947, 59, 199, 19777, 419, 263, 20359, 47, 1759, 19, 947, 1291, 59, 199, 569, 23813, 19777, 20173,...

			11 is in the sequence because the Collatz trajectory of 11 is 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 and the sum of the odd terms is 11 + 17 + 13 + 5 + 1 = 47 is prime.

Cf. A033493, A225748.

lst={};coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&];a:=Select[coll[n],OddQ[#]&];Do[s=Sum[a[[i]],{i,1,Length[a]}];If[PrimeQ[s],AppendTo[lst,n]],{n,1,500}];lst

A275114 Primes p for which the sum of the numbers in the Collatz iteration (A033493) of p is a prime.

Original entry on oeis.org

2, 67, 149, 163, 229, 359, 373, 401, 571, 719, 727, 827, 919, 941, 1031, 1049, 1129, 1153, 1201, 1283, 1307, 1319, 1433, 1453, 1627, 1637, 1987, 2017, 2089, 2137, 2237, 2267, 2281, 2351, 2543, 2617, 2731, 2819, 2851, 2861, 2927, 2969, 3191, 3253, 3581, 3671, 3719

Offset: 1

Jaroslav Krizek, Jul 17 2016

nonn

Primes p such that A033493(p) is a prime.

Prime terms from A225748.

			Prime 67 with Collatz trajectory (67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1) is a term because A033493(67) = 1459 (prime).

Eric Weisstein's World of Mathematics, Collatz Problem
Wikipedia, Collatz conjecture

Cf. A033493, A225748.

[n: n in [1..4000] | IsPrime(&+[k eq 1 select n else IsOdd(Self(k-1)) and not IsOne(Self(k-1)) select 3*Self(k-1)+1 else Self(k-1) div 2: k in [1..5*n]]) and IsPrime(n)];

Select[Prime@ Range@ 540, PrimeQ[Total@ FixedPointList[Which[# == 1, 1, EvenQ@ #, #/2, True, 3 # + 1] &, #] - 1] &] (* Michael De Vlieger, Jul 17 2016, after Alonso del Arte at A033493 *)

cp's OEIS Frontend

A274243 Numbers n for which the sum of the odd numbers in the Collatz (3x+1) iteration of n is prime.

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