The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A356108

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A356108

Numbers == 2 (mod 6) that cannot be written as p^2 + q where p and q are primes.
(history; published version)

#6 by N. J. A. Sloane at Tue Aug 23 10:18:16 EDT 2022

STATUS

proposed

approved

#5 by Robert Israel at Wed Jul 27 16:29:42 EDT 2022

STATUS

editing

proposed

#4 by Robert Israel at Wed Jul 27 16:29:29 EDT 2022

COMMENTS

There are many numbers == 0 (mod 6) that cannot be written as p^2 + q, but nearly all of them are squares.

MAPLE

p:= 2;

do

od

STATUS

proposed

editing

#3 by Robert Israel at Wed Jul 27 00:56:26 EDT 2022

STATUS

editing

proposed

#2 by Robert Israel at Wed Jul 27 00:53:27 EDT 2022

NAME

allocated for Robert IsraelNumbers == 2 (mod 6) that cannot be written as p^2 + q where p and q are primes.

DATA

2, 8, 74, 170, 614, 704, 1010, 24476

OFFSET

1,1

COMMENTS

Numbers k == 2 (mod 6) such that A356077(k/2) = -1.

a(9) > 10^7 if it exists.

EXAMPLE

a(3) = 74 is a term because 74 == 2 (mod 6) and none of 74 - 2^2 = 70, 74 - 3^2 = 65, 74 - 5^2 = 49, 74 - 7^2 = 25 are prime.

MAPLE

filter:= proc(n) local p;

p:= 2;

do

p:= nextprime(p);

if n <= p^2 then return true fi;

if isprime(n-p^2) then return false fi;

od

end proc:

select(filter, [seq(i, i=2..10^6, 6)]);

CROSSREFS

Cf. A356077.

KEYWORD

allocated

nonn,more

AUTHOR

J. M. Bergot and Robert Israel, Jul 27 2022

STATUS

approved

editing

#1 by Robert Israel at Wed Jul 27 00:53:27 EDT 2022

NAME

allocated for Robert Israel

KEYWORD

allocated

STATUS

approved