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 A176229 #11 May 15 2023 19:28:33 %S A176229 7,13,19,37,67,109,127,307,379,487,499,769,877,937,1009,1297,1567, %T A176229 2269,2389,2659,2857,3037,3187,3457,3847,3907,3919,4447,4789,4969, %U A176229 4999,5077,5167,5347,5737,6007,6997,7039,7669,8689,8779,9199,10597,11467,11827 %N A176229 The smaller members p of cousin prime pairs (p,p+4) with a semiprime arithmetic mean p+2. %C A176229 By definition a subsequence of A063637 and of A023200. %C A176229 The associated p+4 are members of A063638. %C A176229 Because all members of A023200 are == 1 (mod 3), the semiprimes p+2 are all == 0 (mod 3), so one of their two factors is 3. %C A176229 The least-significant digit (LSD) of p > 13 in A023200 is always 3, 7 or 9, but those with LSD equal to 3 demand p+2 to have LSD 5 and therefore divisor 5 which contradicts the semiprime property above, so 13 is the only member of the sequence with LSD equal to 3. %H A176229 Amiram Eldar, <a href="/A176229/b176229.txt">Table of n, a(n) for n = 1..10000</a> %e A176229 7 = prime(4), 11 = prime(5), (7+11)/2 = 3^2 = semiprime(3), so 7 is in the sequence. %e A176229 13 = prime(6), 17 = prime(7), (13+17)/3 = 3 * 5 = semiprime(6), so 13 is in the sequence. %e A176229 19 = prime(8), 23 = prime(9), (19+23)/3 = 3 * 7 = semiprime(7), so 19 is in the sequence. %t A176229 aQ[n_] := PrimeQ[n] && PrimeOmega[n + 2] == 2 && PrimeQ[n + 4]; Select[Range[12000], aQ] (* _Amiram Eldar_, Sep 08 2019 *) %t A176229 Select[Prime[Range[1500]],PrimeQ[#+4]&&PrimeOmega[#+2]==2&] (* _Harvey P. Dale_, May 15 2023 *) %Y A176229 Cf. A001358, A023200, A046132, A063637, A063638. %K A176229 nonn %O A176229 1,1 %A A176229 Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 12 2010