A327581 - OEIS

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A327581

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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..31.

Pierre CAMI, PFGW Script

PROG

(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

CROSSREFS

Sequence in context: A215616 A249737 A129205 * A098173 A180977 A371761

Adjacent sequences: A327578 A327579 A327580 * A327582 A327583 A327584

KEYWORD

nonn

AUTHOR

Pierre CAMI, Sep 17 2019

STATUS

approved