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).

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

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

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Enrique Navarrete, Scatterplots of Sequence 4n+1/(smallest prime divisor) and Relationship to Prime Sequence

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

Cf. A002144.

Sequence in context: A206435 A080797 A358440 * A085910 A093544 A082983

Adjacent sequences: A280815 A280816 A280817 * A280819 A280820 A280821

Keyword

nonn

Author

Enrique Navarrete, Jan 17 2017

Status

approved