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A330288 Start with the list of numbers from 1 to n. As long as the list has odd and even elements, append to the list the sum of the smallest odd and smallest even elements, taken with multiplicity, and delete these terms from the list. a(n) is the largest element in the final list. 1
1, 3, 3, 10, 15, 21, 17, 21, 19, 29, 29, 49, 47, 49, 91, 75, 73, 75, 73, 75, 73, 75, 73, 75, 73, 75, 123, 121, 135, 135, 131, 135, 131, 131, 163, 157, 153, 157, 187, 193, 181, 193, 215, 223, 213, 213, 277, 275, 243, 243, 321, 299, 289, 291, 261, 265, 261, 265, 261 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Conjecture: a(4)=10 is the only even term. - Jon E. Schoenfield, Dec 28 2019
LINKS
EXAMPLE
To find a(8), create the list {1, 2, 3, 4, 5, 6, 7, 8}. Remove from this list the least odd element (1) and the least even element (2) and insert their sum 1 + 2 = 3, to get the new list {3, 3, 4, 5, 6, 7, 8}. The least odd element (3) is present twice, the least even element (4) once. Remove all these from the list and insert their sum, 3 + 3 + 4 = 10, to get the new list {5, 6, 7, 8, 10}. Now, the least odd element is 5 and the least even element is 6. Add them to get the list {7, 8, 10, 11}. Now, replace 7 and 8 with their sum and the list becomes {10, 11, 15}. Replace 10 and 11 with their sum and the list becomes {15, 21}. There is no even element left, so a(8) = 21, the largest element in the list.
MATHEMATICA
Array[FixedPoint[If[AnyTrue[{#2, #3}, ! IntegerQ@ # &], {Max@ #1}, Sort@ {Delete[#1, #3], #2} & @@ {#1, #2 Count[#1, #2] + #3 Count[#1, #3], Position[#1, k_ /; ! FreeQ[{#2, #3}, k]]}] & @@ {#, SelectFirst[#, OddQ], SelectFirst[#, EvenQ]} &, Range@ #][[1]] &, 59] (* Michael De Vlieger, Dec 14 2019 *)
PROG
(PARI) apply( A330288(n)={ my( even=[1..n\2]*2, odd=[ 2*k-1 | k<-[1..n\/2]],
keep(S)=[t | t<-S, t>S[1]], s); while( even && odd,
s = even[1]*(#even - #even=keep(even)) + odd[1]*(#odd - #odd=keep(odd));
if( s%2, odd=vecsort(concat(odd, s)), even=vecsort(concat(even, s)) ));
if( odd, vecmax(odd), vecmax(even))}, [1..99]) \\ M. F. Hasler, Dec 08 2019
CROSSREFS
Sequence in context: A277963 A193965 A301279 * A262923 A367301 A319882
KEYWORD
nonn
AUTHOR
Ali Sada, Dec 09 2019
EXTENSIONS
Definition and terms corrected by M. F. Hasler
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)