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.
The POBAs for 1 start with 3/2, 2/3, 5/7, 13/11, 11/13, 19/17, 17/19, 31/29, 29/31, 43/41, 41/43, 61/59, 59/61. For example, if p and q are primes and q > 13, then 11/13 is closer to 1 than p/q is.
x = 1; z = 200; p[k_] := p[k] = Prime[k];
t = Table[Max[Table[NextPrime[x*p[k], -1]/p[k], {k, 1, n}]], {n, 1, z}];
d = DeleteDuplicates[t]; tL = Select[d, # > 0 &] (* lower POBA *)
t = Table[Min[Table[NextPrime[x*p[k]]/p[k], {k, 1, n}]], {n, 1, z}];
d = DeleteDuplicates[t]; tU = Select[d, # > 0 &] (* upper POBA *)
v = Sort[Union[tL, tU], Abs[#1 - x] > Abs[#2 - x] &];
b = Denominator[v]; s = Select[Range[Length[b]], b[[#]] == Min[Drop[b, # - 1]] &];
y = Table[v[[s[[n]]]], {n, 1, Length[s]}] (* POBA, A265759/A265760 *)
Numerator[tL] (* A001359 *)
Denominator[tL] (* A006512 *)
Numerator[tU] (* A006512 *)
Denominator[tU] (* A001359 *)
Numerator[y] (* A265759 *)
Denominator[y] (* A265760 *)
For p = 3, 3p - 2 = 7; for p = 523, 3p - 2 = 1567.
a088878 n = a088878_list !! (n-1) a088878_list = filter ((== 1) . a010051' . subtract 2 . (* 3)) a000040_list -- Reinhard Zumkeller, Jul 02 2015
[ p: p in PrimesUpTo(770) | IsPrime(3*p-2) ]; // Klaus Brockhaus, Dec 21 2008
lst={};Do[p=Prime[n];If[PrimeQ[3*p-2],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 22 2008 *)
n = 1; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, (Prime[k] + 2n)/(2n + 1)]], {k, 1, 500}]; a (* Artur Jasinski, Dec 12 2007 *)
Select[Prime[Range[150]],PrimeQ[3#-2]&] (* Harvey P. Dale, Feb 27 2024 *)
list(lim)=select(p->isprime(3*p-2),primes(primepi(lim))) \\ Charles R Greathouse IV, Jul 25 2011
a(7) = 3*23 + 2 = 71.
a094524 = (+ 2) . (* 3) . a023208 -- Reinhard Zumkeller, Aug 15 2011
Select[Table[3*Prime[n]+2,{n,200}],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)
forprime(p=2,600,if(isprime(q=3*p+2),print1(q,",")))
A136061:=Filtered(Filtered([1..10^6],IsPrime),p->IsPrime((p+4)/5)); # Muniru A Asiru, Oct 10 2017
n = 2; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a
Select[Prime[Range[400]], PrimeQ[(# + 4) / 5]&] (* Vincenzo Librandi, Apr 14 2013 *)
{forprime(p=1,1e4/*default(primelimit)*/, p%5-1 & next; isprime(p\5+1) & print1(p","))} \\ M. F. Hasler, Feb 26 2012
n = 7; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a
[p: p in PrimesInInterval(6, 1200000) | IsPrime((p+1) div 2) and IsPrime((p+2) div 3) and IsPrime((p+3) div 4)]; // Vincenzo Librandi, Apr 09 2013
lst={};Do[p=Prime[n];If[PrimeQ[(p+1)/2]&&PrimeQ[(p+2)/3]&&PrimeQ[(p+3)/ 4],AppendTo[lst,p]],{n,2*9!}];lst
is(n)=n%120==1 && isprime(n) && isprime(n\2+1) && isprime(n\3+1) && isprime(n\4+1) \\ Charles R Greathouse IV, Nov 30 2016
from sympy import prime, isprime A163573_list = [4*q-3 for q in (prime(i) for i in range(1,10000)) if isprime(4*q-3) and isprime(2*q-1) and (not (4*q-1) % 3) and isprime((4*q-1)//3)] # Chai Wah Wu, Nov 30 2016
n = 2; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, (Prime[k] + 2n)/(2n + 1)]], {k, 1, 1500}]; a
(* Second program: *)
Select[Prime@ Range@ 250, PrimeQ[5 # - 4] &] (* Michael De Vlieger, Aug 04 2017 *)
lista(nn) = forprime(p=2, nn, if (isprime(5*p-4), print1(p, ", ")))
n = 3; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, (Prime[k] + 2n)/(2n + 1)]], {k, 1, 1500}]; a
n = 3; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a
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