A023133 Signature sequence of Pi (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

1, 2, 3, 4, 1, 5, 2, 6, 3, 7, 4, 1, 8, 5, 2, 9, 6, 3, 10, 7, 4, 1, 11, 8, 5, 2, 12, 9, 6, 3, 13, 10, 7, 4, 1, 14, 11, 8, 5, 2, 15, 12, 9, 6, 3, 16, 13, 10, 7, 4, 1, 17, 14, 11, 8, 5, 2, 18, 15, 12, 9, 6, 3, 19, 16, 13, 10, 7, 4, 1, 20, 17, 14, 11, 8, 5, 2, 21, 18, 15, 12, 9, 6, 3

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

References

• C. Kimberling, "Fractal Sequences and Interspersions", Ars Combinatoria, vol. 45 p 157 1997.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• C. Kimberling, Interspersions
• Index entries for sequences related to signature sequences

Crossrefs

Cf. A001840, A008810.

Programs

PARI

lista(nn) = {v = vector(nn^2, k, kij = k+nn-1; i = 1+(kij % nn); j = kij\nn; i+j*Pi); vs = vecsort(v, , 1); for (k=1, #vs, print1(curi = 1+((vs[k]+nn-1) % nn), ", "); if (curi == nn, break));} \\ Michel Marcus, Apr 10 2015