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A098059
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Primes preceding gaps divisible by 4.
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6
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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
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OFFSET
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1,1
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COMMENTS
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Prime complement of A098058. - Robert G. Wilson v, Jul 17 2015
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) ~ 2n log n. - Charles R Greathouse IV, Jun 29 2015
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EXAMPLE
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7 is a term since the next prime after 7 is 11 and 11-7 is divisible by 4.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A001223, A098058.
Sequence in context: A344045 A048646 A152087 * A078860 A029710 A145897
Adjacent sequences: A098056 A098057 A098058 * A098060 A098061 A098062
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard, Sep 11 2004
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EXTENSIONS
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Edited by Ray Chandler, Oct 26 2006
New name from Robert Israel and Charles R Greathouse IV, Jun 29 2015
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STATUS
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approved
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