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 A219528 #18 Apr 07 2025 09:49:38
%S A219528 2,3,5,7,11,13,17,19,23,31,37,47,53,71,73,97,107,109,127,163,191,193,
%T A219528 257,383,431,433,487,577,647,769,863,971,1151,1153,1297,1459,2591,
%U A219528 2593,2917,3457,3889,4373,6143,6911,8191,8747,10369,12289,13121,15551,17497,18433,23327,27647,39367,52489,62207,65537,73727
%N A219528 Primes neighboring a 3-smooth number.
%C A219528 Prime numbers of the form of 2^j*3^k +/- 1, which may be called "near-3-smooth primes".
%C A219528 Such prime numbers can often be proved prime by OpenPFGW.
%H A219528 Lei Zhou, <a href="/A219528/b219528.txt">Table of n, a(n) for n = 1..10000</a>
%e A219528 a(1)=2=1+1, where A003586(1)=1;
%e A219528 a(2)=3=2+1, where A003586(2)=2;
%e A219528 ...
%e A219528 a(59)=73727=2^13*3^2-1, where A003586(97)=2^13*3^2=73728.
%t A219528 f[n_] := Block[{p2, p3 = 3^Range[0, Floor@ Log[3, n] + 1]}, p2 = 2^Floor[Log[2, n/p3] + 1]; Min[ Select[ p2*p3, IntegerQ]]];
%t A219528 a={};ct=0;tsm=1;While[ct<59,cp=tsm-1;If[(PrimeQ[cp])&&(!MemberQ[a,cp]),a=Append[a,cp];ct++];cp=cp+2;If[(PrimeQ[cp])&&(!MemberQ[a,cp]),a=Append[a,cp];ct++];tsm=f[tsm]];Print[a]
%o A219528 (PARI) list(lim)=my(v=List([2]), N); for(n=0, log(lim\2)\log(3), N=2*3^n; while(N<=lim, if(ispseudoprime(N-1),listput(v, N-1)); if(ispseudoprime(N+1), listput(v, N+1)); N<<=1)); vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, Nov 21 2012
%Y A219528 Cf. A003586
%K A219528 nonn
%O A219528 1,1
%A A219528 _Lei Zhou_, Nov 21 2012