This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: The sequence is finite. LINKS 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. A007095, A293142. 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: A091923 A050719 A217062 * A244913 A098415 A067283 Adjacent sequences:  A293659 A293660 A293661 * A293663 A293664 A293665 KEYWORD nonn,base AUTHOR Felix FrÃ¶hlich, Dec 30 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)