A112594 Natural function used for generating x^2 and sqrt(x) only using iteration and Q(x) (the characteristic function of sqrt).

0, 3, 4, 5, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86

Offset

0,2

Comments

The sequence can be defined as follows: a(0) = 0, a(n+1) = b(a(n)) where b(n) = n + 2*Q(n+4) + 1 (Q is given in A010052)

References

R. M. Robinson, Primitive Recursive Functions, Bulletin of the American Mathematical Society, Vol. 53 (1947), pp. 925-942.

Links

Table of n, a(n) for n=0..70.

Formula

a(n) = n + 2*floor(sqrt(n)) = n+2*A000196(n).

Crossrefs

Cf. A010052.

Sequence in context: A334631 A105020 A286053 * A188003 A120519 A100614

Adjacent sequences: A112591 A112592 A112593 * A112595 A112596 A112597

Keyword

nonn

Author

Daniel E. Severin (danielseverin(AT)yahoo.es), Dec 24 2005

Status

approved