A076561 -id:A076561 - cp's OEIS frontend

A362138 a(n) = gpf(a(n-1) + prime(n)) where gpf is the greatest prime factor and a(1)=2.

2, 5, 5, 3, 7, 5, 11, 5, 7, 3, 17, 3, 11, 3, 5, 29, 11, 3, 7, 13, 43, 61, 3, 23, 5, 53, 13, 5, 19, 11, 23, 11, 37, 11, 5, 13, 17, 5, 43, 3, 13, 97, 3, 7, 17, 3, 107, 11, 17, 41, 137, 47, 3, 127, 3, 19, 3, 137, 23, 19, 151, 37, 43, 59, 31, 29, 5, 19, 61, 41, 197

Offset: 1

Sebastian F. Orellana, Jun 12 2023

nonn

			a(3) = gpf(a(2) + prime(3)) = gpf(5+5) = 5.

Sebastian F. Orellana, Table of n, a(n) for n = 1..10000

Cf. A006530 (gpf), A000040.

Cf. A076560, A076561.

gpf[n_] := FactorInteger[n][[-1, 1]]; a[1] = 2; a[n_] := a[n] = gpf[a[n - 1] + Prime[n]]; Array[a, 100] (* Amiram Eldar, Jun 15 2023 *)

from sympy import factorint, prime
list=[2]
num=1
k=50
for i in range(0, k):
  list.append(max(factorint(list[i]+prime(i+1))))
print(list)

A132850 a(0)=1; a(n) = the smallest prime dividing (n+a(n-1)), for n>=1.

Original entry on oeis.org

1, 2, 2, 5, 3, 2, 2, 3, 11, 2, 2, 13, 5, 2, 2, 17, 3, 2, 2, 3, 23, 2, 2, 5, 29, 2, 2, 29, 3, 2, 2, 3, 5, 2, 2, 37, 73, 2, 2, 41, 3, 2, 2, 3, 47, 2, 2, 7, 5, 2, 2, 53, 3, 2, 2, 3, 59, 2, 2, 61, 11, 2, 2, 5, 3, 2, 2, 3, 71, 2, 2, 73, 5, 2, 2, 7, 83, 2, 2, 3, 83, 2, 2, 5, 89, 2, 2, 89, 3, 2, 2, 3, 5, 2, 2

Offset: 0

Leroy Quet, Nov 21 2007

nonn

a(4n+1) = a(4n+2) = 2, for all n >= 0. a(4n) and a(4n+3) are odd primes, for all n >= 0.

			a(8) + 9 = 11 + 9 = 20. The smallest prime divisor of 20 is 2. So a(9) = 2.

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

Cf. A076561.

a = {1}; Do[AppendTo[a, FactorInteger[n + a[[ -1]]][[1, 1]]], {n, 1, 100}]; a (* Stefan Steinerberger, Nov 25 2007 *)
nxt[{n_,a_}]:={n+1,FactorInteger[n+1+a][[1,1]]}; Transpose[NestList[nxt,{0,1},100]][[2]] (* Harvey P. Dale, Jan 21 2015 *)

More terms from Stefan Steinerberger, Nov 25 2007

cp's OEIS Frontend

A362138 a(n) = gpf(a(n-1) + prime(n)) where gpf is the greatest prime factor and a(1)=2.

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