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 A152127 #16 Feb 16 2025 08:33:09
%S A152127 28,766,34522,1706602,107863996,7379208796,542100094312,
%T A152127 41248685420836,3233516261489332,260607555289408894,
%U A152127 21446383929686290726,1795656778320649469818,152541729206365604807782
%N A152127 Sum of cousin primes < 10^n.
%C A152127 Cousin primes are prime pairs that differ by 4. The convention here is to count a cousin pair as long as the first cousin of the pair is less than or equal to the specified bound which in this sequence is 10^n.
%C A152127 "According to the first Hardy-Littlewood conjecture, the cousin primes have the same asymptotic density as the twin primes." See the MathWorld link. The (sum of cousin prime pairs < 10^n)/4 ~ number of cousin primes < 10^2n.
%H A152127 Cino Hilliard, <a href="http://groups.google.com/group/sumprimes/web/sum-of-cousin-primes--10-n">Gcc Sum of cousin primes</a>. [broken link]
%H A152127 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CousinPrimes.html">Cousin Primes</a>.
%e A152127 (3,7) and (7,11) are the cousin primes < 10. These add up to 28 the first entry in the sequence.
%o A152127 (PARI) lista(pmax) = {my(sm = 10, prev = 2, pow = 10); forprime(p = 3, pmax, if(p == prev + 4, sm += (prev + p)); if(p > pow, print1(sm, ", "); pow *= 10); prev = p);} \\ _Amiram Eldar_, Jul 06 2024
%Y A152127 Cf. A023200, A046132, A080840, A152052.
%K A152127 nonn,more
%O A152127 1,1
%A A152127 _Cino Hilliard_, Nov 25 2008
%E A152127 Data corrected by _Amiram Eldar_, Jul 06 2024