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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

If a(n)=2, then corresponding prime-difference is a power of 2.

a(n)=2 for twin-prime differences.

LINKS

Table of n, a(n) for n=2..106.

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

Cf. A001223, A006530, A081413, A000230.

Sequence in context: A352201 A052298 A179938 * A082863 A278950 A029411

Adjacent sequences: A081409 A081410 A081411 * A081413 A081414 A081415

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 02 2003

STATUS

approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)