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A086002 Primes which when added to their own rotation yield a prime. 7
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

EXAMPLE

a(100)=12917 because (i) 12917 is prime and (ii) rotate(12917) = 17912 and 12917+17912=30829, which is also prime.

MAPLE

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

CROSSREFS

Cf. A086003, A086004.

Sequence in context: A098246 A091551 A033528 * A061783 A140017 A119711

Adjacent sequences:  A085999 A086000 A086001 * A086003 A086004 A086005

KEYWORD

base,nonn

AUTHOR

Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 07 2003

EXTENSIONS

Edited by R. J. Mathar, May 27 2009

STATUS

approved

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)