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A081412
Largest prime divisors of differences between consecutive primes.
1
2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 7, 2, 3, 2, 5, 2, 3, 3, 2, 3, 3, 2, 5, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 5, 3, 3, 3, 2, 3, 2, 2, 5, 7, 2, 2, 2, 7, 3, 5, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 5, 2, 5, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 3, 5, 3, 3, 2, 3, 5
OFFSET
2,1
COMMENTS
If a(n)=2, then corresponding prime-difference is a power of 2.
a(n)=2 for twin-prime differences.
FORMULA
a(n) = A006530(A001223(n)).
MATHEMATICA
Table[FactorInteger[Prime[w+1]-Prime[w]][[ -1, 1]], {w, 2, 256}]
FactorInteger[#][[-1, 1]]&/@Differences[Prime[Range[2, 110]]] (* Harvey P. Dale, Sep 24 2017 *)
PROG
(PARI) a(n) = vecmax(factor(prime(n+1)-prime(n))[, 1]); \\ Michel Marcus, Mar 27 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 02 2003
STATUS
approved