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A236075 Odd primes p with prime(2*p) - 2*prime(p) and prime(p) - 2*prime((p-1)/2) both prime. 3
5, 29, 79, 101, 103, 109, 353, 487, 821, 1367, 1811, 2111, 2593, 2617, 2939, 2969, 3001, 3659, 3727, 3877, 3911, 5347, 5779, 6481, 6959, 7121, 9059, 9649, 10007, 10099, 11299, 11311, 11827, 12343, 12511, 12539, 12589, 12689, 12923, 13781, 13967, 14249, 15859, 15923, 16363, 16889, 17321, 17683, 17881, 18181 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By the conjecture in A236074, this sequence should have infinitely many terms.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 5 since neither prime(2*2) - 2*prime(2) = 1 nor  prime(3) - 2*prime((3-1)/2) = 1 is prime, but prime(2*5) - 2*prime(5) = 29 - 2*11 = 7 and prime(5) - 2*prime((5-1)/2) = 11 - 2*3 = 5 are both prime.

MATHEMATICA

PQ[n_]:=n>0&&PrimeQ[n]

p[n_]:=PQ[Prime[2n]-2Prime[n]]&&PQ[Prime[n]-2*Prime[(n-1)/2]]

n=0; Do[If[p[Prime[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 2, 10^6}]

PROG

(PARI) s=[]; forprime(p=3, 20000, if(isprime(prime(2*p)-2*prime(p)) && isprime(prime(p)-2*prime((p-1)/2)), s=concat(s, p))); s \\ Colin Barker, Jan 19 2014

CROSSREFS

Cf. A000040, A236074.

Sequence in context: A224498 A087348 A154412 * A272650 A050409 A111937

Adjacent sequences:  A236072 A236073 A236074 * A236076 A236077 A236078

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 19 2014

STATUS

approved

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Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)