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 A271973 Smallest number k such that gcd(s1, s2) = n, where s1 is the sum of the odd numbers and s2 is the sum of the even numbers in the Collatz (3x+1) trajectory of k. 1
 1, 10, 9, 30, 65, 5, 74, 86, 368, 135, 970, 50, 95, 101, 1045, 178, 793, 7, 214, 196, 18, 423, 133, 200, 2572, 629, 621, 358, 700, 451, 3167, 1924, 3611, 1926, 662, 510, 6688, 437, 1525, 5072, 3724, 3161, 1034, 240, 5848, 2487, 704, 442, 19120, 1230, 5138, 3524 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..52. EXAMPLE a(6) = 5 because the Collatz trajectory of 5 is 5 -> 16 -> 8 -> 4 -> 2 -> 1 with s1 = 5+1 = 6 and s2 = 16+8+4+2 = 30 => gcd(6,30) = 6. MAPLE nn:=10^8: for n from 1 to 60 do: ii:=0: for k from 1 to nn while(ii=0) do: kk:=1:m:=k:T[kk]:=k:it:=0: for i from 1 to nn while(m<>1) do: if irem(m, 2)=0 then m:=m/2:kk:=kk+1:T[kk]:=m: else m:=3*m+1:kk:=kk+1:T[kk]:=m: fi: od: s1:=0:s2:=0: for j from 1 to kk do: if irem(T[j], 2)=1 then s1:=s1+T[j]: else s2:=s2+T[j]: fi: od: g:=gcd(s1, s2): if g=n then ii:=1:printf("%d %d \n", n, k): else fi: od: od: MATHEMATICA Table[k = 1; While[n != GCD[Total@ Select[#, OddQ], Total@ Select[#, EvenQ]] &@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, k, # > 1 &], k++]; k, {n, 52}] (* Michael De Vlieger, Jul 13 2016 *) CROSSREFS Cf. A213909, A213916. Sequence in context: A003568 A305196 A099642 * A237114 A217412 A241285 Adjacent sequences: A271970 A271971 A271972 * A271974 A271975 A271976 KEYWORD nonn AUTHOR Michel Lagneau, Jul 13 2016 STATUS approved

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Last modified November 28 19:28 EST 2023. Contains 367419 sequences. (Running on oeis4.)