A280818 - OEIS

%I #44 Sep 25 2023 17:47:47

%S 1,5,3,13,17,7,5,29,11,37,41,15,7,53,19,61,13,23,73,11,27,17,89,31,97,

%T 101,35,109,113,39,11,25,43,19,137,47,29,149,51,157,23,55,13,173,59,

%U 181,37,63,193,197,67,41,19,71,31,17,75,229,233,79,241,49,83,23,257

%N a(0)=1; for n > 0, if 4n+1 is prime, then a(n)=4n+1, otherwise a(n)=(4n+1)/LPF(4n+1).

%C Scatter graph consists of points on rays from the origin with slopes of the following approximate values (measured around n=1000): 4 for primes, 1.3337 for terms a(n) whose least prime factor (LPF) is 3, 0.8002 for terms whose LPF is 5, 0.5716 for terms whose LPF is 7, etc. (see link).

%C The first 100 terms of the sequence include all odd primes through prime(33) = 137; the first 1000 terms of the sequence include all odd primes through prime(218) = 1361; prime(33)/100 = 137/100 = 1.37, and prime(218)/1000 = 1361/1000 = 1.361.

%H Harvey P. Dale, <a href="/A280818/b280818.txt">Table of n, a(n) for n = 0..1000</a>

%H Enrique Navarrete, <a href="/A280818/a280818.pdf">Scatterplots of Sequence 4n+1/(smallest prime divisor) and Relationship to Prime Sequence</a>

%t nxt[{n_,a_}]:={n+1,If[PrimeQ[4n+5],4n+5,(4n+5)/FactorInteger[4n+5][[1,1]]]}; NestList[nxt,{0,1},70][[;;,2]] (* _Harvey P. Dale_, Sep 25 2023 *)

%o (PARI) a(n) = {if (n==0, 1, x = 4*n+1; f = factor(x); if (isprime(x), x, x/f[1,1]););} \\ _Michel Marcus_, Jan 22 2017

%Y Cf. A002144.

%K nonn

%O 0,2

%A _Enrique Navarrete_, Jan 17 2017