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A346675
First differences of A088176.
0
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
1,1
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.
FORMULA
a(n) = A088176(n+2) - A088176(n+1).
EXAMPLE
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.
MATHEMATICA
Differences[NextPrime/@Select[Prime@Range[500], NextPrime[#, -1]==#-2&]] (* Giorgos Kalogeropoulos, Jul 28 2021 *)
CROSSREFS
Cf. A088176.
Sequence in context: A081732 A079033 A272771 * A077038 A053320 A351649
KEYWORD
nonn,easy
AUTHOR
Luca Santarsiero, Jul 28 2021
STATUS
approved