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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

%I

%S 1,2,4,6,8,10,12,14,18,22,26,28,30,32,36,40,44,48,50,54,58,60,62,66,

%T 76,78,82,84,94,96,98,100,102,104,114,116,120,126,132,136,138,140,144,

%U 150,154,158,162,166,170,176,184,188,190,198,202,204,208,210,212,216,220

%N 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).

%C All terms except 1 are even. - _Robert Israel_, Apr 07 2019

%H Robert Israel, <a href="/A058218/b058218.txt">Table of n, a(n) for n = 1..10000</a>

%H Maria Suzuki, <a href="http://www.jstor.org/stable/2589378">Related to Alternative Formulations of the Twin Prime Problem</a>, American Math. Monthly, 107 (2000) pp. 55-56.

%p filter:= proc(n)

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

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

%p end proc:

%p select(filter, [\$1..1000]); # _Robert Israel_, Apr 07 2019

%t 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;

%t Select[Range[1000], filterQ] (* _Jean-François Alcover_, Aug 16 2020, after _Robert Israel_ *)

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

%Y Includes 2*A124518.

%K nonn

%O 1,2

%A _John W. Layman_, Nov 30 2000

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Last modified July 28 23:07 EDT 2021. Contains 346340 sequences. (Running on oeis4.)