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A327581
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a(1) is the smallest prime p such that 6*p^2-1 and 6*p^2+1 are twin primes; for n > 1, a(n) is the smallest prime q > a(n-1) such that 6*q^prime(n)-1 and 6*q^prime(n)+1 are twin primes or 0 if no solution exists.
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1
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5, 0, 2557, 51137, 52057, 55373, 88867, 95273, 179947, 236653, 993647, 1010467, 1935533, 2031767, 2138803, 2849317, 8031343, 11696563, 11715133, 18125993, 22615493, 26766633, 26801393, 29963077, 39377893, 58282927, 70354657, 98988257, 119772847, 141442493, 145460123
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OFFSET
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1,1
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COMMENTS
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For prime(2) = 3 there is no solution such that 6*q^3-1 and 6*q^3+1 with q prime are twin primes. Because 7 divides 6*p^3-1 when p == 3, 5, 6 mod 7, 7 divides 6*p^3+1 when p == 1, 2, 4 mod 7. Therefore p can only be 7. But then 6*7^3-1 = 11^2*17 and 6*7^3+1 = 29*71 are not prime numbers, so a(2)=0.
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LINKS
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PROG
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(PARI) findp(n, pmin) = {my(pmin = nextprime(pmin+1), q); forprime(p=pmin, , if (isprime(q=6*p^prime(n)-1) && isprime(q+2), return(p)); ); }
lista(nn) = {my(lasta = 2, newa); print1(findp(1, lasta), ", 0"); for (n=3, nn, newa = findp(n, lasta); print1(", ", newa); lasta = newa; ); } \\ Michel Marcus, Sep 20 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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