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 A136204 #8 Nov 21 2023 03:25:38
%S A136204 7,37,127,167,257,337,757,797,887,1307,1597,1657,1667,2347,2557,2897,
%T A136204 2927,3067,4297,4327,4877,5087,5147,5227,5417,5857,6337,6827,6917,
%U A136204 6967,7127,7187,7547,7687,7867,7877,8147,8447,8527,8647,9857,10037,10687
%N A136204 Primes p such that 3p-2 and 3p+2 are primes (see A125272) and its decimal representation ends in 7.
%C A136204 Theorem: If in the triple (3n-2,n,3n+2) all numbers are primes, then n=5 or the decimal representation of n ends in 3 or 7. Proof: Similar to A136191. Alternative Mathematica proof: Table[nn = 10k + r; Intersection (AT)(AT) (Divisors[CoefficientList[(3nn - 2) nn(3nn + 2), k]]), {r, 1, 9, 2}]; This gives {{1, 5}, {1}, {1, 5}, {1}, {1, 5}}. Therefore only r=3 and r=7 allow nontrivial divisors (excluding nn=5 itself).
%H A136204 Robert Israel, <a href="/A136204/b136204.txt">Table of n, a(n) for n = 1..10000</a>
%p A136204 filter:= proc(n) isprime(n) and isprime(3*n-2) and isprime(3*n+2) end proc:
%p A136204 select(filter, [seq(i,i=7..10^4,10)]); # _Robert Israel_, Nov 20 2023
%t A136204 TPrimeQ = (PrimeQ[ # - 2] && PrimeQ[ #/3] && PrimeQ[ # + 2]) &; Select[Select[Range[100000], TPrimeQ]/3, Mod[ #, 10] == 7 &]
%Y A136204 Cf. A136191, A136192, A125272.
%K A136204 nonn,base
%O A136204 1,1
%A A136204 _Carlos Alves_, Dec 21 2007