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A058218 Positive integers that cannot be represented in the form n=5|ab|+a+b for any choice of nonzero integers a and b (positive or negative). 1
1, 2, 4, 6, 8, 10, 12, 14, 18, 22, 26, 28, 30, 32, 36, 40, 44, 48, 50, 54, 58, 60, 62, 66, 76, 78, 82, 84, 94, 96, 98, 100, 102, 104, 114, 116, 120, 126, 132, 136, 138, 140, 144, 150, 154, 158, 162, 166, 170, 176, 184, 188, 190, 198, 202, 204, 208, 210, 212, 216, 220 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All terms except 1 are even. - Robert Israel, Apr 07 2019

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Maria Suzuki, Related to Alternative Formulations of the Twin Prime Problem, American Math. Monthly, 107 (2000) pp. 55-56.

MAPLE

filter:= proc(n)

   nops(select(t -> t mod 5 = 1 or t mod 5 = 4, numtheory:-divisors(5*n+1))) = 2

   and nops(select(t -> t mod 5 = 4, numtheory:-divisors(5*n-1)))=1

end proc:

select(filter, [$1..1000]); # Robert Israel, Apr 07 2019

MATHEMATICA

filterQ[n_] := Length[Select[Divisors[5 n + 1], Mod[#, 5] == 1 || Mod[#, 5] == 4&]] == 2 && Length[Select[Divisors[5 n - 1], Mod[#, 5] == 4&]] == 1;

Select[Range[1000], filterQ] (* Jean-Fran├žois Alcover, Aug 16 2020, after Robert Israel *)

CROSSREFS

A002822 results if the coefficient 5 in the definition above is replaced by 6.

Includes 2*A124518.

Sequence in context: A098807 A189562 A194372 * A264986 A140955 A111905

Adjacent sequences:  A058215 A058216 A058217 * A058219 A058220 A058221

KEYWORD

nonn

AUTHOR

John W. Layman, Nov 30 2000

STATUS

approved

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Last modified April 19 08:01 EDT 2021. Contains 343110 sequences. (Running on oeis4.)