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A367936
Lexicographically earliest sequence of distinct positive integers such that the sum of the distinct prime factors of a(n) + a(n + 1) is a composite number.
1
1, 13, 2, 12, 3, 11, 4, 10, 5, 9, 6, 8, 7, 14, 16, 17, 18, 15, 20, 19, 23, 22, 24, 21, 25, 26, 29, 27, 28, 32, 30, 33, 36, 34, 31, 35, 39, 37, 38, 40, 44, 41, 43, 42, 45, 46, 47, 48, 50, 49, 53, 51, 54, 52, 58, 56, 55, 57, 60, 59, 61, 62, 64, 65, 67, 63, 66, 68, 70, 71, 69, 72, 73, 74, 76, 77, 75, 78, 80, 79, 82
OFFSET
1,2
COMMENTS
The sum of the distinct prime factors of n is sometimes called sopf(n).
LINKS
Éric Angelini, Sums of distinct prime factors, Personal blog, December 2023.
EXAMPLE
a(1) + a(2) = 1 + 13 = 14 whose sopf is 2 + 7 = 9, a composite;
a(2) + a(3) = 13 + 2 = 15 whose sopf is 3 + 5 = 8, a composite;
a(3) + a(4) = 2 + 12 = 14 whose sopf is 2 + 7 = 9, a composite;
a(4) + a(5) = 12 + 3 = 15 whose sopf is 3 + 5 = 8, a composite;
a(13) + a(14) = 7 + 14 = 21 whose sopf is 3 + 7 = 10, a composite; etc.
MATHEMATICA
a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n-1], k]||PrimeQ@Total[First/@FactorInteger[k+a[n-1]]], k++]; k); Array[a, 81]
CROSSREFS
Sequence in context: A317753 A298059 A298708 * A124686 A113807 A008832
KEYWORD
nonn
AUTHOR
STATUS
approved