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%I #33 Mar 03 2024 08:35:34
%S 19,23,29,41,43,47,53,59,61,67,83,89,101,103,107,127,149,157,163,173,
%T 181,191,271,277,307,313,317,331,359,367,379,397,419,479,491,571,577,
%U 593,617,631,673,701,709,727,739,757,761,787,797,811,839,877,907,911
%N Near-miss circular primes: Primes p where all but one of the numbers obtained by cyclically permuting the digits of p are prime.
%C Prime p is a term of the sequence iff A262988(p) = A055642(p) - 1.
%C If a(512) exists, it is larger than 10^16. - _Giovanni Resta_, Apr 27 2017
%C 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
%H Felix Fröhlich and Giovanni Resta, <a href="/A270083/b270083.txt">Table of n, a(n) for n = 1..511</a> (first 487 terms from Felix Fröhlich)
%t 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 *)
%o (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
%o eva(n) = subst(Pol(n), x, 10)
%o 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)
%o forprime(p=1, 1e3, if(is(p), print1(p, ", ")))
%Y Cf. A045978, A068652, A262988.
%K nonn,base
%O 1,1
%A _Felix Fröhlich_, Mar 10 2016
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