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A190799 Primes p=prime(i) such that prime(i+4)-prime(i)=20. 1

%I

%S 47,83,131,137,173,191,251,257,347,419,443,557,587,593,1013,1019,1031,

%T 1049,1217,1301,1427,1433,1439,1979,1997,2069,2267,2531,2657,2687,

%U 2693,2699,2711,3251,3299,3539,4007,4211,4241,4253,4643,4931,5003,5099,5399,5501,5861

%N Primes p=prime(i) such that prime(i+4)-prime(i)=20.

%C Consider sets of 5 consecutive primes with 4 different gaps 2,4,6,8.

%C From 4!=24 cases only 8 gap configurations are possible:

%C {2,4,6,8},{2,4,8,6},{2,6,4,8},{6,2,4,8},

%C {6,8,4,2},{8,4,2,6},{8,4,6,2},{8,6,4,2}.

%C Least sets of 5 consecutive primes with corresponding gap configurations are:

%C {{347,349,353,359,367},{2,4,6,8}}

%C {{1997,1999,2003,2011,2017},{2,4,8,6}}

%C {{10091,10093,10099,10103,10111},{2,6,4,8}}

%C {{8081,8087,8089,8093,8101},{6,2,4,8}}

%C {{83,89,97,101,103},{6,8,4,2}}

%C {{1439,1447,1451,1453,1459},{8,4,2,6}}

%C {{2531,2539,2543,2549,2551},{8,4,6,2}}

%C {{1979,1987,1993,1997,1999},{8,6,4,2}}.

%t p = Prime[Range[1000]]; First /@ Select[Partition[p, 5, 1], Last[#] - First[#] == 20 &] (* _T. D. Noe_, May 23 2011 *)

%Y Only a small part of terms are also in A190792.

%K nonn

%O 1,1

%A _Zak Seidov_, May 20 2011

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Last modified October 24 14:44 EDT 2021. Contains 348233 sequences. (Running on oeis4.)