|
|
A280818
|
|
a(0)=1; for n > 0, if 4n+1 is prime, then a(n)=4n+1, otherwise a(n)=(4n+1)/LPF(4n+1).
|
|
2
|
|
|
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, 101, 35, 109, 113, 39, 11, 25, 43, 19, 137, 47, 29, 149, 51, 157, 23, 55, 13, 173, 59, 181, 37, 63, 193, 197, 67, 41, 19, 71, 31, 17, 75, 229, 233, 79, 241, 49, 83, 23, 257
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
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).
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.
|
|
LINKS
|
|
|
MATHEMATICA
|
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 *)
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|