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A374847
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Numbers k which can be written as k = r+s where r and s are elements of the Collatz trajectory of k.
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2
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2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 78, 80, 81, 82, 84
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OFFSET
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1,1
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COMMENTS
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A trajectory term can be used twice as r = s, so all even numbers are terms (trajectory first term k/2).
The odd terms, which become sparse with increasing size, form A374909.
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LINKS
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EXAMPLE
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2 is a term because its Collatz trajectory is {2, 1} and 2 = 1+1.
21 is not a term: its Collatz trajectory is T = { 21, 64, 32, 16, 8, 4, 2, 1 } and there are no r,s in T with 21 = r+s.
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PROG
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(PARI) is_A374847(k) = { my(T=List(), m=k); while(m>1, if(m%2==0, m=m/2, m=3*m+1); if(m<k, listput(T, m)); ); for(i=1, #T, for(j=i, #T, if(T[i]+T[j]==k, return(1)); )); return(0); }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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