A287865 a(n) = gpf(2*a(n-1)+1), with a(1)=1, where gpf = A006530.

1, 3, 7, 5, 11, 23, 47, 19, 13, 3, 7, 5, 11, 23, 47, 19, 13, 3, 7, 5, 11, 23, 47, 19, 13, 3, 7, 5, 11, 23, 47, 19, 13, 3, 7, 5, 11, 23, 47, 19, 13, 3, 7, 5, 11, 23, 47, 19, 13, 3, 7, 5, 11, 23, 47, 19, 13, 3, 7, 5, 11, 23, 47, 19, 13, 3, 7, 5, 11, 23, 47, 19, 13, 3, 7, 5

Offset: 1

Author

N. J. A. Sloane, Jun 04 2017

Keywords

• nonn
• easy

Comments

Periodic with period length 8.

References

• Oskars Rieksts, Email to N. J. A. Sloane, Jun 04 2017.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Crossrefs

Cf. A006530.

Programs

Maple

gpf:= n->max(1, op(numtheory[factorset](n))); # A006530
a:=[1]; i:=1;
for n from 1 to 100 do i:=gpf(2*i+1); a:=[op(a),i]; od:
a;

Mathematica

LinearRecurrence[PadLeft[{1}, 8], {1, 3, 7, 5, 11, 23, 47, 19, 13}, 100] (* Paolo Xausa, Feb 02 2025 *)

PARI

Vec(x*(1 + 3*x + 7*x^2 + 5*x^3 + 11*x^4 + 23*x^5 + 47*x^6 + 19*x^7 + 12*x^8) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)) + O(x^100)) \\ Colin Barker, Jun 04 2017

Python

from sympy import primefactors
l=[0, 1]
for n in range(2, 77):
    l.append(primefactors(2*l[n - 1] + 1)[-1])
print(l[1:]) # Indranil Ghosh, Jun 04 2017

Formula

From Colin Barker, Jun 04 2017: (Start)

G.f.: x*(1 + 3*x + 7*x^2 + 5*x^3 + 11*x^4 + 23*x^5 + 47*x^6 + 19*x^7 + 12*x^8) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)).

a(n) = a(n-8) for n>9. (End)