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

Author

Cino Hilliard, Sep 11 2004

Keywords

• easy
• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Subsequence of A152087.

Cf. A001223, A098058.

Programs

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 *)

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

Formula

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

Extensions

Edited by Ray Chandler, Oct 26 2006

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