Search: a083990 -id:a083990
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A083989
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Concatenation of prime k and its 10's complement is a prime.
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+10
4
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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43 belongs to this sequence as 4357 is also a prime.
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MAPLE
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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
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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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
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graph;
refs;
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MAPLE
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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
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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