

A306247


Numbers k such that 2k  p is not a prime where p is any prime divisor of 4k^2  1.


2



1, 2, 3, 6, 9, 14, 15, 19, 21, 26, 29, 30, 34, 36, 40, 48, 49, 51, 54, 61, 63, 64, 69, 74, 75, 79, 82, 84, 86, 89, 90, 95, 96, 99, 103, 106, 110, 111, 112, 114, 119, 120, 135, 139, 141, 146, 147, 149, 151, 152, 153, 154, 156, 161, 166, 169, 173, 174, 179, 180, 184, 186, 187, 190, 194
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OFFSET

1,2


COMMENTS

Primes in a(n): 2, 3, 19, 29, 61, 79, 89, 103, 139, 149, 151, 173, 179, ...


LINKS

Table of n, a(n) for n=1..65.


FORMULA

A306261(a(n)) > 1 for n >= 4.


EXAMPLE

1 is a term because 4*1^2  1 = 3 and 2*1  3 = 1 (nonprime);
2 is a term because 4*2^2  1 = 15 and 2*2  15 = 11 (nonprime);
3 is a term because 4*3^2  1 = 35 and 2*3  35 = 29 (nonprime);
6 is a term because 4*6^2  1 = 143 = 11*13 and 2*6  11 = 1 (nonprime), 2*6  13 = 1 (nonprime);
9 is a term because 4*9^2  1 = 323 = 17*19 and 2*9  17 = 1 (nonprime), 2*9  19 = 1 (nonprime).


MAPLE

filter:= proc(n) andmap(`not` @ isprime, map(p > 2*np, numtheory:factorset(4*n^21))) end proc:
select(filter, [$1..300]); # Robert Israel, Jan 31 2019


MATHEMATICA

Select[Range@ 200, AllTrue[2 #  FactorInteger[4 #^2  1][[All, 1]], ! PrimeQ@ # &] &] (* Michael De Vlieger, Feb 03 2019 *)


PROG

(PARI) isok(k) = {my(pf = factor(4*k^21)[, 1]); #select(x>isprime(2*kx), pf) == 0; } \\ Michel Marcus, Mar 02 2019


CROSSREFS

Includes A040040.
Cf. A306261.
Sequence in context: A309897 A128955 A215523 * A244739 A075123 A023559
Adjacent sequences: A306244 A306245 A306246 * A306248 A306249 A306250


KEYWORD

nonn,easy


AUTHOR

JuriStepan Gerasimov, Jan 31 2019


STATUS

approved



