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%I #11 Oct 30 2022 18:13:53
%S 2,3,4,8,12,20,32,54,94,170,297,549,1017,1895,3505,6577,12388,23565,
%T 44891,85922,164299,314173,602624,1158231,2232286
%N Number of Sophie Germain primes <= prime(2^n).
%C Sophie Germain primes are primes p such that 2p+1 is also prime.
%e The first four primes are 2, 3, 5 and 7. Three of these are Sophie Germain primes (since 2*2 + 1 = 5, 2*3 + 1 = 7 and 2*5 + 1 = 11 are prime, but 2*7 + = 15). Therefore the second value in the sequence is 3.
%t << NumberTheory`NumberTheoryFunctions` cnt = 0; currentPrime = 1; For[ i = 1, i == i, i ++, currentPrime = NextPrime[ currentPrime ]; If[ PrimeQ[ 2*currentPrime + 1 ], cnt++ ]; If[ IntegerQ[ Log[ 2, i ] ], Print[ cnt ] ]; ]
%Y Cf. A049040.
%K nonn
%O 1,1
%A _Alexander D. Healy_, Mar 19 2001
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