A219528 - OEIS

%I #15 Nov 23 2012 19:35:29

%S 2,3,5,7,11,13,17,19,23,31,37,47,53,71,73,97,107,109,127,163,191,193,

%T 257,383,431,433,487,577,647,769,863,971,1151,1153,1297,1459,2591,

%U 2593,2917,3457,3889,4373,6143,6911,8191,8747,10369,12289,13121,15551,17497,18433,23327,27647,39367,52489,62207,65537,73727

%N Primes neighboring a 3-smooth number.

%C Prime numbers of the form of 2^j*3^k +/- 1, which may be called "Near-3-smooth primes".

%C Such prime numbers can often be proved prime by OpenPFGW.

%H Lei Zhou, <a href="/A219528/b219528.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1)=2=1+1, where A003586[1]=1;

%e a(2)=3=2+1, where A003586[2]=2;

%e ...

%e a(59)=73727=2^13*3^2-1, where A003586[97]=2^13*3^2=73728

%t 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 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 (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 Cf. A003586

%K nonn

%O 1,1

%A _Lei Zhou_, Nov 21 2012