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A236143 Odd primes p with prime(p-1) - (p-1) and prime(p-1) - 2*prime((p-1)/2) both prime. 2
7, 11, 31, 67, 179, 193, 197, 281, 347, 349, 563, 599, 757, 1123, 1453, 1543, 1933, 1987, 2083, 2531, 2971, 3037, 3259, 3547, 3583, 3701, 3919, 4027, 4483, 5023, 5581, 5591, 5647, 5981, 6449, 7207, 7297, 7603, 8291, 9049 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
By part (i) of the conjecture in A236138, this sequence should have infinitely many terms.
LINKS
EXAMPLE
a(1) = 7 with prime(6) - 6 = 13 - 6 = 7 and prime(6) - 2*prime(3) = 13 - 2*5 = 3 both prime.
MATHEMATICA
PQ[n_]:=n>0&&PrimeQ[n]
p[n_]:=PrimeQ[Prime[n-1]-(n-1)]&&PQ[Prime[n-1]-2*Prime[(n-1)/2]]
n=0; Do[If[p[Prime[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 2, 10^5}]
PROG
(PARI) s=[]; forprime(p=3, 10000, if(isprime(prime(p-1)-(p-1)) && isprime(prime(p-1)-2*prime((p-1)/2)), s=concat(s, p))); s \\ Colin Barker, Jan 19 2014
CROSSREFS
Sequence in context: A291349 A293046 A213176 * A084443 A228029 A053711
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 19 2014
STATUS
approved

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Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)