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A053615 Pyramidal sequence: distance to nearest product of two consecutive integers (promic or heteromecic numbers). 6
0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(A002378(n))=0; a(n^2)=n.

Table A049581 T(n,k) = |n-k| read by sides of squares from T(1,n) to T(n,n), then from T(n,n) to T(n,1). - Boris Putievskiy, Jan 29 2013

LINKS

Table of n, a(n) for n=0..103.

Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.

FORMULA

a(n) = A004738(n+1) - 1.

Let u(1)=1, u(n) = n - u(n-sqrtint(n)) (cf. A037458); then a(0)=0 and for n > 0 a(n) = 2*u(n) - n. - Benoit Cloitre, Dec 22 2002

a(0)=0 then a(n) = floor(sqrt(n)) - a(n - floor(sqrt(n))). - Benoit Cloitre, May 03 2004

a(n) = |A196199|. a(n) = |n - t*t - t - 1|, where t = floor(sqrt(n-1)). - Boris Putievskiy, Jan 29 2013

EXAMPLE

a(10) = |10 - 3*4| = 2.

From Boris Putievskiy, Jan 29 2013: (Start)

The start of the sequence as table:

  0, 1, 2, 3, 4, 5, 6, 7, ...

  1, 0, 1, 2, 3, 4, 5, 6, ...

  2, 1, 0, 1, 2, 3, 4, 5, ...

  3, 2, 1, 0, 1, 2, 3, 4, ...

  4, 3, 2, 1, 0, 1, 2, 3, ...

  5, 4, 3, 2, 1, 0, 1, 2, ...

  6, 5, 4, 3, 2, 1, 0, 1, ...

  ...

The start of the sequence as triangle array read by rows:

  0;

  1, 0, 1;

  2, 1, 0, 1, 2;

  3, 2, 1, 0, 1, 2, 3;

  4, 3, 2, 1, 0, 1, 2, 3, 4;

  5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5;

  6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6;

  7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7;

  ...

Row number r contains 2*r-1 numbers: r-1, r-2, ..., 0, 1, 2, ..., r-1. (End)

MATHEMATICA

a[0] = 0; a[n_] := Floor[Sqrt[n]] - a[n - Floor[Sqrt[n]]]; Table[a[n], {n, 0, 103}] (* Jean-Fran├žois Alcover, Dec 16 2011, after Benoit Cloitre *)

PROG

(PARI) a(n)=if(n<1, 0, sqrtint(n)-a(n-sqrtint(n)))

CROSSREFS

Cf. A002262, A002378, A004738, A049581, A053188, A196199.

Sequence in context: A228110 A255175 A196199 * A002819 A037834 A212496

Adjacent sequences:  A053612 A053613 A053614 * A053616 A053617 A053618

KEYWORD

easy,nice,nonn

AUTHOR

Henry Bottomley, Mar 20 2000

STATUS

approved

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Last modified October 23 04:00 EDT 2017. Contains 293783 sequences.