A098059 Primes preceding gaps divisible by 4.

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

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

Subsequence of A152087.

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