cp's OEIS Frontend

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.

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

This page as a plain text file.
%I A083991 #9 Aug 07 2015 03:01:52
%S A083991 3,7,17,29,71,83,281,719,983,997,1637,2309,3701,4493,5507,6299,7691,
%T A083991 8363,9161,9803,11003,13163,17117,18371,20807,31181,31793,32693,32843,
%U A083991 33617,33893,34211,34673,37277,38453,49409,50591,61547,62723,65327
%N A083991 Members of A083989 whose 10's complement is also a member of A083989.
%H A083991 Diana Mecum, <a href="/A083991/b083991.txt">Table of n, a(n) for n = 1..341</a>
%e A083991 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.
%e A083991 17 and 83 both are members and are each other's 10's complement.
%p A083991 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
%Y A083991 Cf. A083989, A083990.
%K A083991 base,nonn
%O A083991 1,1
%A A083991 _Amarnath Murthy_, May 23 2003
%E A083991 More terms from _Diana L. Mecum_ and _R. J. Mathar_, Jul 18 2007