This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049040 #24 Jul 25 2025 06:51:46
%S A049040 1,6,26,167,1222,9668,82237,711154,6284076,56325540,510628554,
%T A049040 4672267109
%N A049040 Number of Sophie Germain primes <= prime(10^n).
%C A049040 Sophie Germain primes are primes p such that 2p+1 is also prime.
%H A049040 <a href="/index/Pri#primepop">Index entries for sequences related to numbers of primes in various ranges</a>.
%e A049040 The first 10 primes are 2,3,5,7,11,13,17,23,29 and 31. 6 of these are Sophie Germain primes, namely: 2,3,5,11,23 and 29.
%t A049040 cnt = 0; currentPrime = 1; For[ i = 1, i == i, i ++, currentPrime = NextPrime[ currentPrime ]; If[ PrimeQ[ 2*currentPrime + 1 ], cnt++ ]; If[ IntegerQ[ Log[ 10, i ] ], Print[ cnt ] ]; ]
%o A049040 (PARI) list(len) = {my(c = 0, k = 0, pow = 1, pmax = prime(pow)); forprime(p = 1, , if(isprime(2*p+1), c++); if(p == pmax, print1(c, ", "); k++; if(k == len, break); pow *= 10; pmax = prime(pow)));} \\ _Amiram Eldar_, Jul 25 2025
%Y A049040 Cf. A005384, A006988.
%K A049040 nonn,more
%O A049040 0,2
%A A049040 Dennis S. Kluk (mathemagician(AT)ameritech.net)
%E A049040 More terms from _Alexander D. Healy_, Mar 19 2001
%E A049040 Offset changed to 0, a(0) prepended and a(9)-a(11) added by _Amiram Eldar_, Jul 25 2025