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.
3 = 2*2^0+1 is a term and 2/2 = 1 = 2^0. 7 = 3*2^1+1 is a term and 6/3 = 2 = 2^1. 13 = 3*2^2+1 is a term and 12/3 = 4 = 2^2. 41 = 5*2^3+1 is a term and 40/5 = 8 = 2^3. 113 = 7*2^4+1 is a term and 112/7 = 16 = 2^4.
alias(pf = NumberTheory:-PrimeFactors): gpf := n -> max(pf(n)):
is_a := n -> isprime(n) and pf((n-1)/gpf(n-1)) = {2}:
3, op(select(is_a, [$3..919])); # Peter Luschny, Dec 14 2020
Select[Range[3, 1000], PrimeQ[#] && !CompositeQ[(# - 1)/2^IntegerExponent[(# - 1), 2]] &] (* Amiram Eldar, Dec 28 2018 *)
The 10th term is 13, the first term in 1024-Germain prime sequence: {13,19,37,79,223,...}. The largest prime was found for 2^79: both 1427 and 604462909807314587353088*1427 + 1 = 862568572295037916152856577 are primes.
Table[p = 2; While[! PrimeQ[2^n*p + 1], p = NextPrime@ p]; p, {n, 0, 71}] (* Michael De Vlieger, Mar 05 2017 *)
P=10^6;
default(primelimit,P);
a(n)={my(N=2^n);forprime(p=2,P,if(isprime(N*p+1),return(p)));}
vector(66,n,a(n))
/* Joerg Arndt, Jun 18 2012 */
a(9) = 2048 because 2047 = 23 * 89, 2048 = 2^11 and 11 - 2 = 9.
with(numtheory): P:=proc(q) local a,b,k,v; v:=array(0..100); for k from 0 to 100 do v[k]:=0; od; a:=0; for k from 2 to q do b:=bigomega(k); if v[abs(b-a)]=0 then v[abs(b-a)]:=k; fi; a:=b; od; k:=0; while v[k]>0 do print(v[k]); k:=k+1; od; print(); end: P(10^6);
s = PrimeOmega@ Range[10^6]; 1 + First /@ Values@ KeySort@ PositionIndex@ Flatten@ Map[Abs@ Differences@ # &, Partition[s, 2, 1]] (* Michael De Vlieger, Apr 26 2017, Version 10 *)
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