A060200 Number of Sophie Germain primes <= prime(2^n).

2, 3, 4, 8, 12, 20, 32, 54, 94, 170, 297, 549, 1017, 1895, 3505, 6577, 12388, 23565, 44891, 85922, 164299, 314173, 602624, 1158231, 2232286

Offset

1,1

Comments

Sophie Germain primes are primes p such that 2p+1 is also prime.

Links

Table of n, a(n) for n=1..25.

Example

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.

Mathematica

<< 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 ] ]; ]

Crossrefs

Cf. A049040.

Sequence in context: A222125 A222126 A004045 * A057608 A060984 A226947

Adjacent sequences: A060197 A060198 A060199 * A060201 A060202 A060203

Keyword

nonn

Author

Alexander D. Healy, Mar 19 2001

Status

approved