A114015 Quaternary emirpimes.

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

Offset: 1

Author

Jonathan Vos Post, Jun 13 2006

Keywords

• base
• easy
• nonn
• less

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.

Examples

			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.
		

Links

• Eric Weisstein, Jonathan Vos Post, et al., Emirpimes.
• Eric Weisstein's World of Mathematics, Quaternary.

Crossrefs

Cf. A001358, A004086, A007090, A097393.

Programs

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

Formula

a(n) = A007090(i) for some i in A001358 and R(a(n)) = A007090(j) for some j =/= i in A001358. a(n) = A007090(i) for some i in A001358 and A004086(a(n)) = A007090(j) for some j =/= i in A001358.

Extensions

1102 inserted by R. J. Mathar, Dec 22 2010