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A293662
Base-9 circular primes that are not base-9 repunits.
7
11, 13, 17, 19, 23, 37, 43, 47, 67, 71, 73, 79, 101, 149, 173, 181, 211, 233, 347, 421, 443, 613, 641, 647, 673, 719, 727, 971, 1123, 1361, 1429, 1609, 1697, 2153, 2179, 3371, 3547, 3833, 4019, 4091, 4099, 4229, 5227, 5261, 5281, 5683, 5689, 5741, 5749, 5821
OFFSET
1,1
COMMENTS
Conjecture: The sequence is finite.
EXAMPLE
101 written in base 9 is 122. The base-9 numbers 122, 221, 212 written in base 10 are 101, 181, 173, respectively and all those numbers are prime, so 101, 173 and 181 are terms of the sequence.
MATHEMATICA
With[{b = 9}, Select[Prime@ Range[PrimePi@ b + 1, 10^3], Function[w, And[AllTrue[Array[FromDigits[RotateRight[w, #], b] &, Length@ w - 1], PrimeQ], Union@ w != {1} ]]@ IntegerDigits[#, b] &]] (* Michael De Vlieger, Dec 30 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
decimal(v, base) = my(w=[]); for(k=0, #v-1, w=concat(w, v[#v-k]*base^k)); sum(i=1, #w, w[i])
is_circularprime(p, base) = my(db=digits(p, base), r=rot(db), i=0); if(vecmin(db)==0, return(0), while(1, dec=decimal(r, base); if(!ispseudoprime(dec), return(0)); r=rot(r); if(r==db, return(1))))
forprime(p=1, , if(vecmin(digits(p, 9))!=vecmax(digits(p, 9)), if(is_circularprime(p, 9), print1(p, ", "))))
CROSSREFS
Cf. base-b nonrepunit circular primes: A293657 (b=4), A293658 (b=5), A293659 (b=6), A293660 (b=7), A293661 (b=8), A293663 (b=10).
Sequence in context: A046501 A050719 A217062 * A244913 A098415 A329176
KEYWORD
nonn,base
AUTHOR
Felix Fröhlich, Dec 30 2017
STATUS
approved