A367935 Lexicographically earliest sequence of distinct positive integers such that the sum of the distinct prime factors of a(n) + a(n + 1) is a prime.

1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 12, 11, 13, 14, 15, 16, 18, 19, 17, 20, 21, 22, 25, 23, 24, 26, 27, 31, 28, 30, 29, 32, 35, 33, 34, 37, 36, 43, 38, 41, 39, 40, 42, 46, 50, 47, 49, 48, 52, 44, 45, 51, 56, 53, 54, 55, 58, 60, 61, 57, 59, 62, 63, 64, 67, 69, 68, 71, 65, 66, 70, 72, 77, 74, 75, 76, 73, 78, 79, 81, 82

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 +  2 =  3 whose sopf is  3, a prime number;
a(2) + a(3) =  2 +  3 =  5 whose sopf is  5, a prime number;
a(7) + a(8) =  7 +  9 = 16 whose sopf is  2, a prime number;
a(8) + a(9) =  9 +  8 = 17 whose sopf is 17, a prime number;
a(9) + a(10) = 8 + 10 = 18 whose sopf is  2 + 3 = 5, a prime number; 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

Cf. A008472, A367936.

Sequence in context: A356759 A372656 A375184 * A207334 A294660 A180198

Adjacent sequences: A367932 A367933 A367934 * A367936 A367937 A367938

Keyword

nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Dec 05 2023

Status

approved