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A047972 Distance of n-th prime to nearest square. 5
1, 1, 1, 2, 2, 3, 1, 3, 2, 4, 5, 1, 5, 6, 2, 4, 5, 3, 3, 7, 8, 2, 2, 8, 3, 1, 3, 7, 9, 8, 6, 10, 7, 5, 5, 7, 12, 6, 2, 4, 10, 12, 5, 3, 1, 3, 14, 2, 2, 4, 8, 14, 15, 5, 1, 7, 13, 15, 12, 8, 6, 4, 17, 13, 11, 7, 7, 13, 14, 12, 8, 2, 6, 12, 18, 17, 11, 3, 1, 9, 19, 20, 10, 8, 2, 2, 8, 16, 20, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

FORMULA

For each prime, find the closest square (preceding or succeeding); subtract, take absolute value.

EXAMPLE

For 13, 9 is the preceding square, 16 is the succeeding. 13-9 = 4, 16-13 is 3, so the distance is 3.

MATHEMATICA

a[n_] := (p = Prime[n]; ns = p+1; While[ !IntegerQ[ Sqrt[ns++]]]; ps = p-1; While[ !IntegerQ[ Sqrt[ps--]]]; Min[ ns-p-1, p-ps-1]); Table[a[n], {n, 1, 90}] (* Jean-Fran├žois Alcover, Nov 18 2011 *)

Table[Apply[Min, Abs[p - Through[{Floor, Ceiling}[Sqrt[p]]]^2]], {p, Prime[Range[90]]}] (* Jan Mangaldan, May 07 2014 *)

Min[Abs[#-Through[{Floor, Ceiling}[Sqrt[#]]]^2]]&/@Prime[Range[100]] (* More concise version of program immediately above *) (* Harvey P. Dale, Dec 04 2019 *)

CROSSREFS

Cf. A047973.

Sequence in context: A171691 A088904 A241568 * A004595 A071681 A135621

Adjacent sequences:  A047969 A047970 A047971 * A047973 A047974 A047975

KEYWORD

easy,nonn,nice

AUTHOR

Enoch Haga, Dec 11 1999

STATUS

approved

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Last modified February 23 23:18 EST 2020. Contains 332195 sequences. (Running on oeis4.)