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A031217 Number of terms in longest arithmetic progression of consecutive primes starting at n-th prime (conjectured to be unbounded). 1
2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) <= 4 for n <= 10^5. - Reinhard Zumkeller, Feb 02 2007

The first instance of 4 consecutive primes in an arithmetic progression is (251, 257, 263, 269), which starts with the 54th prime.  The first instance of 5 consecutive primes in an arithmetic progression is (9843019, 9843049, 9843079, 9843109, 9843139), which starts with the 654926th prime. [From Harvey P. Dale, Jul 13 2011]

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, A6.

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primes in arithmetic progressions

EXAMPLE

At 47 there are 3 consecutive primes in A.P., 47 53 59.

MATHEMATICA

max = 5; a[n_] := Catch[pp = NestList[ NextPrime, Prime[n], max-1]; Do[ If[ Length[ Union[ Differences[pp[[1 ;; -k]] ] ] ] == 1, Throw[max-k+1]], {k, 1, max-1}]]; Table[a[n], {n, 1, 105}] (* Jean-Fran├žois Alcover, Jul 17 2012 *)

PROG

(PARI) a(n)=my(p=prime(n), q=nextprime(p+1), g=q-p, k=2); while(nextprime(q+1)==q+g, q+=g; k++); k \\ Charles R Greathouse IV, Jun 20 2013

CROSSREFS

Cf. A001223.

Sequence in context: A090387 A030329 A120881 * A078545 A111497 A220554

Adjacent sequences:  A031214 A031215 A031216 * A031218 A031219 A031220

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers

STATUS

approved

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Last modified September 17 11:28 EDT 2014. Contains 246841 sequences.