A317921 a(1) = a(2) = 1; for n >= 3, a(n) = 3*a(t(n)) - a(n-t(n)) where t = A004001.

1, 1, 2, 2, 5, 5, 4, 4, 13, 13, 10, 7, 7, 7, 8, 8, 35, 35, 26, 17, 8, 8, 8, 8, 11, 14, 17, 17, 17, 17, 16, 16, 97, 97, 70, 43, 16, -11, -11, -11, -11, -11, -2, 7, 16, 25, 34, 43, 43, 43, 43, 43, 43, 43, 40, 37, 34, 31, 31, 31, 31, 31, 32, 32, 275, 275, 194, 113, 32, -49, -130, -130, -130, -130, -130

Offset: 1

Author

Altug Alkan, Aug 11 2018

Keywords

• sign
• look

Comments

Sequence has a fractal-like structure. Each generation (between consecutive powers of 2) provides a pattern which looks like an EKG signal since maximum value of a(n) (in corresponding generation) is damped step by step.

Links

• Altug Alkan, Table of n, a(n) for n = 1..32768
• Altug Alkan, Line plot of a(n) for n <= 2^17

Crossrefs

Cf. A004001, A317648, A317754.

Programs

PARI

t=vector(99); t[1]=t[2]=1; for(n=3, #t, t[n] = t[n-t[n-1]]+t[t[n-1]]); a=vector(99); a[1]=a[2]=1; for(n=3, #a, a[n] = 3*a[t[n]]-a[n-t[n]]); a