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A098429 Number of cousin prime pairs (p, p+4) with p <= n. 4

%I #16 May 28 2017 09:07:55

%S 0,0,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,

%T 4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,

%U 7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,10,10

%N Number of cousin prime pairs (p, p+4) with p <= n.

%C Convention: a prime pair is <= n iff its smallest member is <= n.

%C Except for (3, 7), there is only 1 pair congruence class for cousin primes, i.e. (+1, -1) (mod 6). [_Daniel Forgues_, Aug 05 2009]

%H Daniel Forgues, <a href="/A098429/b098429.txt">Table of n, a(n) for n=1..99996</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CousinPrimes.html">Cousin Primes</a>

%e First cousin prime pairs: (3,7),(7,11),(13,17),(19,23), ...

%e therefore the sequence starts: 0 0 1 1 1 1 2 2 2 2 2 2 3 ...

%t Accumulate[Table[If[PrimeQ[i]&&PrimeQ[i+4],1,0],{i,1,100}]] (* _Seiichi Kirikami_, May 28 2017 *)

%Y Cf. A023200, A046132, A098428, A071538.

%K nonn

%O 1,7

%A _Reinhard Zumkeller_, Sep 07 2004

%E Edited by _Daniel Forgues_, Aug 01 2009

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Last modified April 24 18:17 EDT 2024. Contains 371962 sequences. (Running on oeis4.)