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A086002
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Primes which when added to their own rotation yield a prime.
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7
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229, 239, 241, 257, 269, 271, 277, 281, 439, 443, 463, 467, 479, 499, 613, 641, 653, 661, 673, 677, 683, 691, 811, 823, 839, 863, 881, 10111, 10151, 10169, 10181, 10243, 10247, 10253, 10267, 10303, 10313, 10331, 10343, 10391, 10429, 10453, 10457
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OFFSET
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1,1
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COMMENTS
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Let rotation rot(k) of a number k be defined by swapping the blocks of the first [d/2] and of the last [d/2] digits of k, where d=A055642(k). If the number of digits in k is odd, the center digit remains untouched during rotation.
So for example the rotation of 1234 is 3412, while the rotation of 12345 is 45312.
Rotation differs from reversal (A004086) for numbers with at least 4 digits, that is, after A004087(168) if we are concerned with primes.
The sequence lists primes p such that p+rot(p) is (again) prime.
Differs from A061783, where rot(k) is replaced by reverse(k), from the 5-digit terms on. - M. F. Hasler, Mar 03 2011
a(n) has an odd number of digits (see RJM comment in A086004). If a(n) has 2m+1 digits, then the m-th digit of a(n) is even as otherwise a(n) + rot(a(n)) is even. - Chai Wah Wu, Aug 19 2015
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LINKS
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EXAMPLE
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a(100)=12917 because (i) 12917 is prime and (ii) rotate(12917) = 17912 and 12917+17912=30829, which is also prime.
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MAPLE
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A055642 := proc(n) max(1, 1+ilog10(n)) ; end:
rot := proc(n) local d, dl, dh, pre, suf ; d := A055642(n) ; dl := floor( d/2) ; dh := floor( (d+1)/2) ; pre := floor(n/10^dh) ; suf := n mod 10^dl ; if dl <> dh then suf*10^dh+pre+10^dl*( floor(n/10^dl) mod 10) ; else suf*10^dh+pre ; fi; end:
isA086002 := proc(p) if isprime(p) then isprime(p+rot(p)) ; else false; fi; end:
for n from 1 to 1500 do p := ithprime(n) ; if isA086002(p) then printf("%d, ", p) ; fi; od: # R. J. Mathar, May 27 2009
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MATHEMATICA
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rot[n_]:=Module[{idn=IntegerDigits[n], len}, len=Length[idn]; If[OddQ[len], FromDigits[ Join[Take[idn, -Floor[len/2]], {idn[[(len+1)/2]]}, Take[idn, Floor[len/2]]]], FromDigits[ Join[ Take[ idn, -len/2], Take[idn, len/2]]]]]; Select[Prime[Range[1500]], PrimeQ[ #+rot[#]]&] (* Harvey P. Dale, Apr 26 2022 *)
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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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Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 07 2003
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EXTENSIONS
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STATUS
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approved
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