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A103875
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Numbers k such that 2*P(k) + 5, 2*P(k+1) + 7, 2*P(k+2) + 9, 2*P(k+3) + 11 are also consecutive primes where P(i) = i-th prime.
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2
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43465, 79433, 82148, 300879, 584423, 609169, 631181, 704593, 1293377, 1393266, 1939691, 2203731, 2396444, 2585471, 3224519, 3533876, 3687348, 3951399, 4094469, 4239250, 4442048, 4648592, 4744723, 5076823, 5190219, 5397694, 6779299, 7850072, 7942431, 8679283, 8851519
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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cpQ[n_]:=Module[{p=Prime[n], a, b, c, d}, a=2p+5; b=2Prime[n+1]+7; c= 2*Prime[n+2]+9; d=2Prime[n+3]+11; AllTrue[{a, b, c, d}, PrimeQ]&&b== NextPrime[a]&&c==NextPrime[b]&&d==NextPrime[c]]; Select[Range[10^6], cpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 14 2017 *)
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PROG
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(PARI) lista(nn) = {my(k=1, v=[2, 3, 5, 7]); forprime(p=11, nn, k++; v=concat(v[2..4], p); if(ispseudoprime(2*v[1]+5) && nextprime(2*v[1]+6)==2*v[2]+7 && nextprime(2*v[2]+8)==2*v[3]+9 && nextprime(2*v[3]+10)==2*v[4]+11, print1(k, ", "))); } \\ Jinyuan Wang, Mar 05 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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