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A270083
Near-miss circular primes: Primes p where all but one of the numbers obtained by cyclically permuting the digits of p are prime.
14
19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 101, 103, 107, 127, 149, 157, 163, 173, 181, 191, 271, 277, 307, 313, 317, 331, 359, 367, 379, 397, 419, 479, 491, 571, 577, 593, 617, 631, 673, 701, 709, 727, 739, 757, 761, 787, 797, 811, 839, 877, 907, 911
OFFSET
1,1
COMMENTS
Prime p is a term of the sequence iff A262988(p) = A055642(p) - 1.
If a(512) exists, it is larger than 10^16. - Giovanni Resta, Apr 27 2017
If one of the digits is even or 5, the miss occurs when that digit is permuted to the ones place. Avoiding that simple obstruction, this sequence intersected with A091633 is 19, 173, 191, 313, 317, 331, 379, 397, 739, 797, 911, 937, 977, 1319, 1777, 1913, 1979, 1993, 3191, 3373, 3719, 3733, 3793, ... . Is this an infinite subsequence? - Danny Rorabaugh, May 15 2017
LINKS
Felix Fröhlich and Giovanni Resta, Table of n, a(n) for n = 1..511 (first 487 terms from Felix Fröhlich)
MATHEMATICA
NearCircPrmsUpTo10powerK[k_]:= Union @ Flatten[ Table[ParallelMap[If[(Count[FromDigits /@ NestList[RotateLeft, IntegerDigits[#], IntegerLength[#]-1], _?PrimeQ] == IntegerLength[#]-1), #, Nothing] &, Select[FromDigits /@ Tuples[Range[0, 9], n], PrimeQ]], {n, k}], 1]; NearCircPrmsUpTo10powerK[7] (* Mikk Heidemaa, Apr 26 2017 *)
PROG
(PARI) rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
eva(n) = subst(Pol(n), x, 10)
is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==#Str(n)-1, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Felix Fröhlich, Mar 10 2016
STATUS
approved