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A098059 Primes preceding gaps divisible by 4. 6
7, 13, 19, 37, 43, 67, 79, 89, 97, 103, 109, 127, 163, 193, 199, 211, 223, 229, 277, 307, 313, 349, 359, 379, 389, 397, 401, 439, 449, 457, 463, 467, 479, 487, 491, 499, 509, 613, 619, 643, 661, 673, 683, 701, 719, 739, 743, 757, 761, 769, 797, 823, 853, 859 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Prime complement of A098058. - Robert G. Wilson v, Jul 17 2015

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) ~ 2n log n. - Charles R Greathouse IV, Jun 29 2015

EXAMPLE

7 is a term since the next prime after 7 is 11 and 11-7 is divisible by 4.

MAPLE

N:= 1000:  # to get all terms up to the second-last prime <= N

Primes:= select(isprime, [2, 2*i+1 $ i=1..floor((N-1)/2)]):

Gaps:= Primes[2..-1] - Primes[1..-2]:

Primes[select(t-> Gaps[t] mod 4 = 0, [$1..nops(Gaps)])]; # Robert Israel, Jun 24 2015

MATHEMATICA

Prime[Select[Range[150], Mod[Prime[ # + 1] - Prime[ # ], 4] == 0 &]] (* Ray Chandler, Oct 26 2006 *)

Transpose[Select[Partition[Prime[Range[200]], 2, 1], Divisible[Last[#]- First[#], 4]&]][[1]] (* Harvey P. Dale, Apr 06 2013 *)

PROG

(PARI) f(n) = for(x=1, n, z=(prime(x+1)-prime(x)); if(z%4==0, print1(prime(x)", ")))

(PARI) p=2; forprime(q=3, 1e4, if((q-p)%4==0, print1(p", ")); p=q) \\ Charles R Greathouse IV, Jun 29 2015

CROSSREFS

Cf. A001223, A098058.

Sequence in context: A344045 A048646 A152087 * A078860 A029710 A145897

Adjacent sequences:  A098056 A098057 A098058 * A098060 A098061 A098062

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Sep 11 2004

EXTENSIONS

Edited by Ray Chandler, Oct 26 2006

New name from Robert Israel and Charles R Greathouse IV, Jun 29 2015

STATUS

approved

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Last modified May 19 13:24 EDT 2022. Contains 353833 sequences. (Running on oeis4.)