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 A034934 #49 May 26 2025 01:57:48
%S A034934 1,3,7,11,15,19,27,31,35,39,47,55,59,67,71,75,87,91,99,111,115,119,
%T A034934 127,131,151,155,159,167,171,175,179,187,195,207,211,231,235,239,255,
%U A034934 259,267,279,287,295,299,307,311,319,327,335,339,347,371,375,379,391
%N A034934 Numbers k such that (3*k + 1)/2 is prime.
%C A034934 Related to hyperperfect numbers of a certain form.
%C A034934 The formula by _Jaroslav Krizek_ is explained as follows: If p = (3n+1)/2 is prime, then it is an integer, and p must be of the form p = 3m-1, i.e., p = A003627(k). On the other hand, if p = A003627(k), then all k < p are coprime to p, so we have B(p) = (Sum_{k<p} k^2)/(Sum_{k<p} k) = (2p-1)/3. This is an integer, since p = 3m-1, and for this number n = (2p-1)/3 = 2m-1, we have that (3n+1)/2 = p is prime. - _M. F. Hasler_, Nov 29 2010
%H A034934 Amiram Eldar, <a href="/A034934/b034934.txt">Table of n, a(n) for n = 1..10000</a>
%H A034934 Judson S. McCranie, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html">A study of hyperperfect numbers</a>, J. Int. Seq., Vol. 3 (2000), Article 00.1.3.
%F A034934 a(n) = A175505(A003627(n)). - _Jaroslav Krizek_, Aug 01 2010
%e A034934 a(6) = 19 because for A003627(6) = 29, B(29) = A053818(29)/A023896(29) = 7714/406 = 19. Cf. A179871-A179891, A003627, A007645. - _Jaroslav Krizek_, Aug 01 2010
%t A034934 Select[Range[500], PrimeQ[(3# + 1)/2] &] (* _Harvey P. Dale_, Jan 15 2011 *)
%o A034934 (Magma) [ n: n in [1..400 by 2] | IsPrime((3*n+1) div 2) ];
%o A034934 (PARI) is(n)=isprime((3*n+1)/2) \\ _Charles R Greathouse IV_, Feb 20 2017
%Y A034934 Cf. A003627, A007645, A038536, A045309, A175505, A179871-A179891.
%K A034934 nonn
%O A034934 1,2
%A A034934 _Jud McCranie_
%E A034934 Corrected by _Vincenzo Librandi_, Mar 24 2010