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 A337673 a(n) is the sum of all positive integers whose Collatz orbit has length n. 1
 0, 1, 2, 4, 8, 16, 37, 74, 172, 344, 786, 1572, 3538, 7206, 16252, 33112, 73762, 149967, 330107, 678610, 1498356, 3082302, 6742487, 13855154, 30122440, 62388962, 135783788, 281177482, 608402189, 1259151448, 2711432766, 5646008216, 12172417990, 25339969480, 54409676729, 113159496364 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) >= 2^(n-1) as 2^(n-1) has orbit length n. LINKS Table of n, a(n) for n=0..35. Index entries for sequences related to 3x+1 (or Collatz) problem EXAMPLE a(6) = 5+32 = 37 as the positive integers whose Collatz orbit has length 6 are {5,32} - the orbit of 5 is 5,16,8,4,2,1, and the orbit of 32 is 32,16,8,4,2,1. PROG (PARI) nextSet(s) = { my(s1 = Set([])); for(i = 1, #s, s1 = setunion(s1, Set([2*s[i]])); if (s[i] > 4 && (s[i]-1) % 3 == 0 && (s[i]-1)/3 % 2 == 1, s1 = setunion(s1, Set([(s[i]-1)/3]))); ); return(s1); } a(n) = { my(s = Set([1])); for(k = 1, n, s = nextSet(s); ); return(sum(i=1, #s, s[i])); } CROSSREFS Cf. A000975, A005186, A153772. Equals row sums of triangles A088975 and A127824. Sequence in context: A095236 A348847 A018536 * A162428 A344491 A028497 Adjacent sequences: A337670 A337671 A337672 * A337674 A337675 A337676 KEYWORD nonn AUTHOR Markus Sigg, Sep 15 2020 EXTENSIONS More terms from David A. Corneth, Sep 15 2020 STATUS approved

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Last modified July 15 21:59 EDT 2024. Contains 374334 sequences. (Running on oeis4.)