A105496 A "Fractal Jump Sequence" (FJS) that reappears twice (itself and itself + 1; see the Comments section).

1, 2, 2, 3, 3, 2, 4, 4, 3, 3, 5, 5, 3, 4, 4, 6, 2, 6, 4, 4, 5, 5, 7, 3, 4, 7, 5, 5, 6, 3, 6, 8, 4, 3, 5, 8, 6, 5, 6, 7, 4, 7, 9, 5, 5, 4, 6, 9, 7, 3, 6, 7, 8, 4, 5, 8, 10, 6, 4, 6, 5, 7, 10, 6, 8, 4, 7, 8, 9, 5, 2, 6, 9, 6, 11, 7, 5, 7, 6, 8, 4, 11, 7, 9, 5

Offset

1,2

Comments

Start on a(1) = 1 and underline it;

from there, jump over 1 term to the right; you land on a(3) = 2, which you underline;

from there, jump over 2 terms to the right; you'll land on a(6) = 2, which you underline;

from there, jump over 2 terms to the right; you'll land on a(9) = 3, which you underline;

from there, jump over 3 terms to the right; you'll land on a(13) = 3, which you underline;

from there, jump over 3 terms to the right; you'll land on a(17) = 2, which you underline; etc.

The underlined terms reproduce the starting sequence. The not underlined terms are the successive terms of the starting sequence augmented by 1.

Links

Dominic McCarty, Table of n, a(n) for n = 1..10000

Prog

(Python)
terms = 20
a, u, i, j, n = {0:1}, {0}, 0, 0, 0
while n < terms:
    n += 2 if n+1 in u else 1
    a[n], k, j = a[i]+1, a[i]+i+1, j+1
    a[k], i = a[j], k
    u.add(k)
print([a[n] for n in range(terms)]) # Dominic McCarty, Mar 31 2025

Crossrefs

Cf. A330639 (multiplying by 2 the non-underlined terms instead of adding 1 to them).

Sequence in context: A154258 A253900 A327487 * A339575 A167618 A211707

Adjacent sequences: A105493 A105494 A105495 * A105497 A105498 A105499

Keyword

nonn,base

Author

Eric Angelini, Dec 22 2019

Extensions

More terms from Dominic McCarty, Mar 31 2025

Status

approved