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A277993 Sophie Germain primes p such that p + 2 and p - 2 are semiprimes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A005384 and A063643.

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..4000

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

(PARI) is(n) = ispseudoprime(n) && ispseudoprime(2*n+1) && bigomega(n+2)==2 && bigomega(n-2)==2 \\ Felix Fröhlich, Nov 07 2016

CROSSREFS

Cf. A005384, A063637, A063638, A063643.

Sequence in context: A104802 A128473 A132235 * A339188 A051650 A049438

Adjacent sequences:  A277990 A277991 A277992 * A277994 A277995 A277996

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Nov 07 2016

STATUS

approved

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Last modified May 21 21:43 EDT 2022. Contains 353929 sequences. (Running on oeis4.)