|
|
A114015
|
|
Quaternary emirpimes.
|
|
0
|
|
|
12, 21, 1022, 1102, 1113, 1222, 1233, 1303, 1313, 1323, 2011, 2012, 2032, 2102, 2201, 2221, 2302, 3031, 3111, 3131, 3231, 3321, 10102, 10213, 10231, 10232, 10233, 10322, 11012, 11033, 11103, 11231, 11321, 11331, 12013, 12022, 12023, 12032
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
These are semiprimes when read as base-4 numbers and their reversals are different semiprimes when read as base-4 numbers. Base-4 analog of what for base 3 is A119684 and for base 10 is A097393. The base-10 representation of this sequence is 6, 9, 74, 87, 106, 111, 115, 119, 123, 133, 134, 142, 146, 161, 169, 178, 205, 213, 221, 237.
|
|
LINKS
|
Eric Weisstein, Jonathan Vos Post, et al., Emirpimes.
Eric Weisstein's World of Mathematics, Quaternary.
|
|
FORMULA
|
|
|
EXAMPLE
|
a(1) = 12 because 12 (base 4) = 6 (base 10) is semiprime and R(12) = 21, where 21 (base 4) = 9 (base 10) is a different semiprime.
a(19) = 3131 because 3131 (base 4) = 221 (base 10) = 13 * 17 (base 10) is semiprime and R(3131) = 1313, where 1313 (base 4) = 119 (base 10) = 7 * 17 (base 10) is a different semiprime.
|
|
MAPLE
|
A007090 := proc(n) local b4; b4 := convert(n, base, 4) ; add( op(i, b4)*10^(i-1), i=1..nops(b4)) ; end proc:
isA114015 := proc(n) local b4; b4rev; if isA001358(n) then b4 := convert(n, base, 4) ; b4rev := add(op(-i, b4)*4^(i-1), i=1..nops(b4)) ; if n = b4rev then false; else isA001358(b4rev) ; end if; else false; end if; end proc:
for n from 1 to 400 do if isA114015(n) then printf("%d, ", A007090(n)) ; end if; end do: # R. J. Mathar, Dec 22 2010
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,easy,nonn,less
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|