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A099655
a[n]=A098085[n]-A096215[n], difference between next and previous primes to A011974[n], the sum of two consecutive primes.
0
4, 4, 2, 2, 6, 2, 6, 2, 6, 2, 4, 6, 6, 8, 4, 4, 14, 4, 2, 10, 6, 6, 6, 10, 2, 12, 12, 12, 12, 2, 6, 6, 6, 10, 14, 4, 14, 14, 10, 4, 8, 6, 6, 8, 8, 10, 6, 8, 8, 2, 12, 8, 8, 6, 12, 18, 18, 10, 6, 6, 6, 2, 2, 12, 12, 6, 12, 8, 10, 8, 10, 8, 4, 6, 8, 4, 14, 12, 2, 2, 14, 14, 14, 14, 2, 20, 20, 8, 10, 8
OFFSET
1,1
FORMULA
a(n)=NextPrime[p(n)+p(n+1)]-PreviousPrime[p(n)+p(n+1)]
EXAMPLE
n=8, p(8)+p(9)=19+23=42,a[8]=43-41=2=a(8).
MATHEMATICA
<<NumberTheory`NumberTheoryFunctions` t1=Table[PreviousPrime[Prime[n]+Prime[n+1]], {n, 1, 128}]; t2=Table[NextPrime[Prime[n]+Prime[n+1]], {n, 1, 128}]; t2-t1
NextPrime[#]-NextPrime[#, -1]&/@(Total/@Partition[Prime[Range[100]], 2, 1]) (* Harvey P. Dale, Mar 07 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 17 2004
STATUS
approved