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A277993
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Sophie Germain primes p such that p + 2 and p - 2 are semiprimes.
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1
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23, 53, 89, 113, 131, 251, 293, 491, 683, 719, 953, 1439, 1499, 1511, 1733, 2393, 3491, 3779, 5171, 7043, 7151, 7433, 7649, 7901, 8069, 8663, 9689, 10781, 12011, 12653, 13049, 13229, 13451, 13553, 14669, 15569, 16001, 16253, 18899, 19709, 20411, 22469, 22751, 23099
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OFFSET
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1,1
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COMMENTS
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Intersection of A005384 and A063643.
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LINKS
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K. D. Bajpai, Table of n, a(n) for n = 1..4000
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EXAMPLE
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a(1) = 23 is Sophie Germain prime because 2*23 + 1 = 47 is prime. Also, 23 + 2 = 25 = 5*5; 23 - 2 = 21 = 7*3; are both semiprime.
a(2) = 53 is Sophie Germain prime because 2*53 + 1 = 107 is prime. Also, 53 + 2 = 55 = 11*5; 23 - 2 = 51 = 17*3; are both semiprime.
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MATHEMATICA
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Select[Select[Prime[Range[10000]], PrimeQ[2 # + 1] &], PrimeOmega[# - 2] == 2 && PrimeOmega[# + 2] == 2 &]
Select[Prime[Range[3000]], PrimeQ[2#+1]&&PrimeOmega[#+{2, -2}]=={2, 2}&] (* Harvey P. Dale, Dec 16 2017 *)
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PROG
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(PARI) is(n) = ispseudoprime(n) && ispseudoprime(2*n+1) && bigomega(n+2)==2 && bigomega(n-2)==2 \\ Felix Fröhlich, Nov 07 2016
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CROSSREFS
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Cf. A005384, A063637, A063638, A063643.
Sequence in context: A104802 A128473 A132235 * A339188 A051650 A049438
Adjacent sequences: A277990 A277991 A277992 * A277994 A277995 A277996
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KEYWORD
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nonn
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AUTHOR
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K. D. Bajpai, Nov 07 2016
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STATUS
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approved
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