

A319630


Positive numbers that are not divisible by two consecutive prime numbers.


5



1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 37, 38, 39, 40, 41, 43, 44, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 76, 79, 80, 81, 82, 83, 85, 86, 87
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OFFSET

1,2


COMMENTS

This sequence is the complement of A104210.
Equivalently, this sequence corresponds to the positive numbers k such that:
 A300820(k) <= 1,
 A087207(k) is a Fibbinary number (A003714).
For any n > 0 and k >= 0, a(n)^k belongs to the sequence.


LINKS

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


FORMULA

A300820(a(n)) <= 1.


EXAMPLE

The number 10 is only divisible by 2 and 5, hence 10 appears in the sequence.
The number 42 is divisible by 2 and 3, hence 42 does not appear in the sequence.


MAPLE

N:= 1000: # for terms <= N
R:= {}:
p:= 2:
do
q:= p; p:= nextprime(p);
if p*q > N then break fi;
R:= R union {seq(i, i=p*q..N, p*q)}
od:
sort(convert({$1..N} minus R, list)); # Robert Israel, Apr 13 2020


PROG

(PARI) is(n) = my (f=factor(n)); for (i=1, #f~1, if (nextprime(f[i, 1]+1)==f[i+1, 1], return (0))); return (1)


CROSSREFS

Cf. A003714, A006094, A087207, A104210, A300820.
Sequence in context: A333559 A153381 A307750 * A324849 A091010 A306528
Adjacent sequences: A319627 A319628 A319629 * A319631 A319632 A319633


KEYWORD

nonn


AUTHOR

Rémy Sigrist, Sep 25 2018


STATUS

approved



