A346675 First differences of A088176.

4, 6, 6, 14, 10, 20, 12, 28, 6, 36, 8, 34, 6, 14, 22, 18, 26, 16, 24, 36, 78, 8, 28, 74, 36, 30, 24, 16, 26, 148, 6, 12, 24, 24, 144, 8, 22, 8, 28, 66, 74, 46, 14, 10, 20, 106, 26, 28, 6, 120, 14, 66, 16, 24, 68, 76, 12, 60, 24, 30, 36, 48, 12, 30, 8, 16, 90, 30

Offset: 1

Author

Luca Santarsiero, Jul 28 2021

Keywords

• nonn
• easy

Comments

Conjecture: each term > 4 appears at least twice.

Every term of the sequence is even, because every term is a difference of two odd primes.

Examples

			a(7) = A088176(9) - A088176(8) = 107 - 79 = 28.
p = 14855077 and q = 14856077 are prime numbers such that the respective preceding prime number is the greater of twin primes. No other prime number between p and q has this property. Thus 1000 is a term of the sequence.
		

Crossrefs

Cf. A088176.

Programs

Mathematica

Differences[NextPrime/@Select[Prime@Range[500],NextPrime[#,-1]==#-2&]] (* Giorgos Kalogeropoulos, Jul 28 2021 *)

Formula

a(n) = A088176(n+2) - A088176(n+1).