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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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, 26 Apr 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

Cf. A045978, A068652, A262988.

Sequence in context: A120640 A309360 A151768 * A286333 A076056 A068654

Adjacent sequences:  A270080 A270081 A270082 * A270084 A270085 A270086

KEYWORD

nonn,base

AUTHOR

Felix Fröhlich, Mar 10 2016

STATUS

approved

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Last modified April 20 18:08 EDT 2021. Contains 343135 sequences. (Running on oeis4.)