A367936 - OEIS

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, 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

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OFFSET

1,2

COMMENTS

The sum of the distinct prime factors of n is sometimes called sopf(n).

LINKS

Table of n, a(n) for n=1..81.

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;