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Search: id:A086002
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| A086002 |
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Primes which when added to their own rotation yield a prime. |
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3
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
Differences to A004086 appear with 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.
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EXAMPLE
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a(100)=12917 because (i) 12917 is prime. (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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CROSSREFS
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Cf. A086003, A086004.
Sequence in context: A098246 A091551 A033528 this_sequence A061783 A140017 A119711
Adjacent sequences: A085999 A086000 A086001 this_sequence A086003 A086004 A086005
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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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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 27 2009
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