cp's OEIS Frontend

The sequence A007069 is an iterated Beatty sequence, like the Wythoff compound sequence (A003622(n)) = (A000201(A000201(n))), and the sequence (A140868(n)) = (A003151(A003151(n))). This sequence is the sequence of first differences 1, 3, 2, 2, 2, 1, 3, 1, 3, 2, ... of A007069.

(a(n)) is a morphic sequence, i.e., the letter-to-letter image of the fixed point of a morphism.

Let theta on {a,b,c,d} be the morphism given by

theta : a->adc, b->adc, c->ad, d->bc.

Let the letter-to-letter morphism lambda be given by

lambda : a->1, b->2, c->2, d->3.

Then (a(n)) = lambda(x), where x = adcbcadadc... is the unique fixed point of theta.

See the appendix of my paper "Morphic words, Beatty sequences...".