A066635 -id:A066635 - cp's OEIS frontend

A080883 Distance of n to next square.

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

Offset: 0

Ralf Stephan, Mar 29 2003

The following sequences all have the same parity: A004737, A006590, A027052, A071028, A071797, A078358, A078446, A080883. - Jeremy Gardiner, Dec 30 2006

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A075555.

Cf. A066635, A053188. - R. J. Mathar, Aug 08 2009

List([0..90], n-> Int(1+RootInt(n))^2 -n); # G. C. Greubel, Nov 07 2019

[Floor(1+Sqrt(n))^2 -n: n in [0..90]]; // G. C. Greubel, Nov 07 2019

A080883 := proc(n) (floor(sqrt(n)+1))^2 -n ; end: seq( A080883(n),n=0..40) ; # R. J. Mathar, Aug 08 2009

Table[Floor[1+Sqrt[n]]^2 -n, {n,0,90}] (* G. C. Greubel, Nov 07 2019 *)

a(n) = (sqrtint(n)+1)^2-n; \\ Michel Marcus, May 22 2024

[floor(1+sqrt(n))^2 -n for n in (0..90)] # G. C. Greubel, Nov 07 2019

a(n) = floor( sqrt(n)+1 )^2 - n.

A163492 Numbers such that the two adjacent integers are a perfect square and a prime.

Original entry on oeis.org

1, 2, 3, 8, 10, 24, 48, 80, 82, 168, 224, 226, 360, 440, 442, 728, 840, 1088, 1090, 1224, 1368, 1522, 1848, 2026, 2208, 2400, 3024, 3250, 3720, 3968, 4760, 5040, 5624, 5928, 6562, 7920, 8648, 9802, 10608, 11026, 11448, 12322, 13688, 13690, 14160, 14640

Offset: 1

Gaurav Kumar, Jul 29 2009

nonn

Also known as the Beprisque numbers.

			a(1) = 2 since 2 lies between 1(square) and 3(prime).
a(2) = 3 since 3 lies between 2(prime) and 4(square).

T. D. Noe, Table of n, a(n) for n = 1..1000
Planet Math, Beprisque numbers

Cf. A051700, A066635.

nn = 100; Sort[Select[Range[0, nn], PrimeQ[#^2 + 2] &]^2 + 1, Select[Range[nn], PrimeQ[#^2 - 2] &]^2 - 1] (* T. D. Noe, Aug 29 2012 *)
Select[Range[15000],AnyTrue[#+{1,-1},PrimeQ]&&AnyTrue[{Sqrt[#-1],Sqrt[ #+1]},IntegerQ]&] (* Harvey P. Dale, Feb 06 2023 *)

Definition clarified by R. J. Mathar, Aug 08 2009

Number 1 added by WG Zeist, Aug 28 2012

A154840 Distance to nearest cube different from n.

Original entry on oeis.org

1, 1, 1, 2, 3, 3, 2, 1, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 37, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

Offset: 0

R. J. Mathar, Nov 01 2009

Equals A074989(n) if this is not zero, else 1+A055400(n-1), the distance to the nearest cube < n.

			a(8)=7, because the two cubes below and above 8 are 1^3=1 and 3^3=27, and the distance to 1 is smaller, namely 8-1=7.

Cf. A066635, A163497.

distNearstDiffCub := proc(n) local iscbr ; iroot(n,3,'iscbr') ; if iscbr then 1+A055400(n-1); else A074989(n) ; end if; end proc;

dnc[n_]:=Module[{c=Surd[n,3]},If[IntegerQ[c],n-(c-1)^3,Min[n-Floor[ c]^3, Ceiling[c]^3-n]]]; Array[dnc,90,0] (* Harvey P. Dale, Mar 30 2019 *)

A289642 Number of 2-digit numbers whose digits add up to n.

Original entry on oeis.org

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

Offset: 1

Miquel Cerda, Jul 09 2017

The 2-digit numbers distributed according to the sum of their digits n.

Symmetrical sequence; a(n) = a(19 - n).

			n(5) = 5 because there are 5 numbers whose digits sum = 5 (14, 23, 32, 41, 50).

Cf. A071817 (3-digit numbers), A090579 (4-digit numbers), A090580 (5-digit numbers), A090581 (6-digit numbers), A278969 (7-digit numbers), A278971 (8-digit numbers), A289354 (9-digit numbers), A053188, A074989, A004739, A066635, A154840, A249121.

G.f.: (1 - x^10)*(x - x^10)/(1 - x)^2.

a(n) = (19-abs(n-9)-abs(n-10))/2 for n=1..18. - Wesley Ivan Hurt, Jul 09 2017

A309914 Distance from n to closest triangular number that is different from n.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 2, 2, 1, 5, 1, 2, 3, 2, 1, 6, 1, 2, 3, 3, 2, 1, 7, 1, 2, 3, 4, 3, 2, 1, 8, 1, 2, 3, 4, 4, 3, 2, 1, 9, 1, 2, 3, 4, 5, 4, 3, 2, 1, 10, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 11, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 12, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 13, 1, 2, 3, 4, 5, 6, 7, 6, 5

Offset: 0

Ilya Gutkovskiy, Aug 22 2019

nonn

Index entries for sequences related to distance to nearest element of some set

Cf. A000217, A053188, A053616, A066635.

a[n_] := Module[{k = 1}, While[! IntegerQ[Sqrt[8 (n + k) + 1]] && ! IntegerQ[Sqrt[8 (n - k) + 1]], k++]; k]; Table[a[n], {n, 0, 100}]

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A080883 Distance of n to next square.

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A163492 Numbers such that the two adjacent integers are a perfect square and a prime.

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A154840 Distance to nearest cube different from n.

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Maple

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A289642 Number of 2-digit numbers whose digits add up to n.

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A309914 Distance from n to closest triangular number that is different from n.

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Mathematica