A083990 -id:A083990 - cp's OEIS frontend

A083989 Concatenation of prime k and its 10's complement is a prime.

3, 7, 17, 23, 29, 31, 41, 43, 53, 67, 71, 83, 109, 127, 139, 151, 173, 179, 197, 211, 229, 263, 271, 281, 307, 359, 463, 547, 557, 569, 587, 593, 673, 677, 683, 691, 701, 719, 727, 757, 769, 823, 839, 881, 883, 887, 907, 937, 983, 997, 1087, 1103, 1171, 1181

Offset: 1

Amarnath Murthy, May 23 2003

			43 belongs to this sequence as 4357 is also a prime.

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

Cf. A083990, A089186.

g:= proc(n) local c; c:= 10^(1+ilog10(n))-n; n*10^(1+ilog10(c))+c end proc:
select(t -> isprime(t) and isprime(g(t)), [seq(i,i=3..10000,2)]); # Robert Israel, Jul 03 2024

More terms from Jason Earls, Jun 01 2003

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

Original entry on oeis.org

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

Amarnath Murthy, May 23 2003

			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.

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

Cf. A083989, A083990.

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

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

cp's OEIS Frontend

A083989 Concatenation of prime k and its 10's complement is a prime.

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