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A115272 Primes p such that p + 2, 18*p^2 + 1, and 18*(p+2)^2 + 1 are all primes. 0
29, 107, 431, 1487, 1607, 2141, 5501, 10139, 10271, 17579, 22481, 23057, 27479, 32369, 36341, 36929, 38447, 55931, 57527, 69827, 75539, 78539, 79691, 81047, 81971, 84179, 86027, 89561, 93761, 102059, 112571, 113147, 118799, 119687 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

a(1)=29 because 31, 18*29^2 + 1 = 15139, and 18*31^2 + 1 = 17299 are all primes.

PROG

(MAGMA) [p: p in PrimesUpTo(200000)| IsPrime(p+2) and IsPrime(18*p^2+1) and IsPrime(18*(p+2)^2+1)] // Vincenzo Librandi, Nov 13 2010

CROSSREFS

Cf. A089001 (Numbers n such that 2*n^2 + 1 is prime),

A090612 (Numbers k such that the k-th prime is of the form 2*k^2+1),

A090698 (Primes of the form 2*n^2+1),

A113541 (Numbers n such that 18*n^2+1 is a multiple of 19).

Sequence in context: A233049 A233050 A142176 * A138716 A276776 A142194

Adjacent sequences:  A115269 A115270 A115271 * A115273 A115274 A115275

KEYWORD

nonn

AUTHOR

Zak Seidov, Jan 19 2006

EXTENSIONS

More terms from Vincenzo Librandi, Mar 27 2010

STATUS

approved

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)