This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
4357 is the term corresponding to 43.
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.
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
a(3) = 17 is a term because 17 is a prime, its 10's complement 83 is a prime, and the concatenations 1783 and 8317 are primes.
filter:= proc(n) local d,c; if not isprime(n) then return false fi; d:= 10^(1+ilog10(n)); c:= d-n; isprime(c) and isprime(c*d+n) and isprime(n*10^(1+ilog10(c))+c) end proc: select(filter, [seq(i,i=3..10000,2)]);
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