A083991 Members of A083989 whose 10's complement is also a member of A083989.

3, 7, 17, 29, 71, 83, 281, 719, 983, 997, 1637, 2309, 3701, 4493, 5507, 6299, 7691, 8363, 9161, 9803, 11003, 13163, 17117, 18371, 20807, 31181, 31793, 32693, 32843, 33617, 33893, 34211, 34673, 37277, 38453, 49409, 50591, 61547, 62723, 65327

Offset: 1

Author

Amarnath Murthy, May 23 2003

Keywords

• base
• nonn

Examples

			Leading zeros are removed before concatenation: 997 is in here because 997 is in A083989 (9973 is prime) and its 10-complement 3 is also in A083989 (37 is prime). Unlike the example of 17 and 83, the 10-complement is not a 1-to-1 relation in cases where 9 shows up as a most significant digit.
17 and 83 both are members and are each other's 10's complement.
		

Links

• Diana Mecum, Table of n, a(n) for n = 1..341

Crossrefs

Cf. A083989, A083990.

Programs

Maple

A055120 := proc(n) local digs ; digs := ilog10(n)+1 ; 10^digs-n ; end: isA083989 := proc(n) local comp,ccat ; if isprime(n) then comp := A055120(n) ; ccat := n*10^(ilog10(comp)+1)+comp ; RETURN( isprime(ccat)) ; else false ; fi ; end: isA083991 := proc(n) local comp; if isA083989(n) then comp := A055120(n) ; RETURN( isA083989(comp) ) ; else false ; fi ; end: for n from 1 to 80000 do if isA083991(n) then printf("%d,",n) ; fi ; od ; # R. J. Mathar, Jul 18 2007

Extensions

More terms from Diana L. Mecum and R. J. Mathar, Jul 18 2007