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Primes p beginning consecutive prime-difference pattern as follows: p, (16, 2, 16, 2), p+36.
5

%I #9 Jan 01 2018 19:41:24

%S 225733,819373,830293,856993,895633,924793,1138393,1210003,1214623,

%T 1353223,1526053,2051443,2183773,2298853,2345443,3169723,3254773,

%U 3287293,3539743,3675613,3847603,4630063,4633003,5137003,5238403

%N Primes p beginning consecutive prime-difference pattern as follows: p, (16, 2, 16, 2), p+36.

%H Harvey P. Dale, <a href="/A067141/b067141.txt">Table of n, a(n) for n = 1..500</a>

%e First term a(1)=p(20082)=225773; it is followed by 225789, 225791, 225807, 225809=p(20086) primes, where the 4 corresponding consecutive differences equal {16, 2, 16, 2}. See analogous cases A022008, A067140.

%t d[x_] := Prime[x+1]-Prime[x] Do[If[Equal[d[n], 16]&&Equal[d[n+1], 2]&& Equal[d[n+2], 16]&&Equal[d[n+3], 2], k=k+1; Print[Prime[n]]], {n, 1, 10000000}]

%t Select[Partition[Prime[Range[400000]],5,1],Differences[#]=={16,2,16,2}&][[All,1]] (* _Harvey P. Dale_, Jan 01 2018 *)

%Y Cf. A001223, A022008, A067140.

%K nonn

%O 1,1

%A _Labos Elemer_, Jan 02 2002