A293660 Base-7 circular primes that are not base-7 repunits.

11, 13, 17, 19, 23, 29, 37, 41, 43, 47, 79, 89, 97, 109, 131, 211, 233, 257, 263, 281, 307, 337, 439, 479, 509, 571, 619, 673, 677, 853, 941, 953, 977, 997, 1021, 1097, 1117, 1163, 1171, 1453, 1511, 1531, 1579, 1597, 1657, 1777, 1787, 1811, 1871, 1933, 1951

Offset

1,1

Comments

Conjecture: The sequence is finite, with 13143449029 being the last term. - [Comment extended by Felix Fröhlich, May 30 2019]

Links

Felix Fröhlich, Table of n, a(n) for n = 1..141

Example

109 written in base 7 is 214. The base-7 numbers 214, 142, 421 written in base 10 are 109, 79, 211, respectively, and all those numbers are prime, so 79, 109 and 211 are terms of the sequence.

Mathematica

With[{b = 7}, Select[Prime@ Range[PrimePi@ b + 1, 300], 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, 7))!=vecmax(digits(p, 7)), if(is_circularprime(p, 7), print1(p, ", "))))

Crossrefs

Cf. A007093, A293142.

Cf. base-b nonrepunit circular primes: A293657 (b=4), A293658 (b=5), A293659 (b=6), A293661 (b=8), A293662 (b=9), A293663 (b=10).

Sequence in context: A244555 A052293 A038842 * A046117 A240900 A091923

Adjacent sequences: A293657 A293658 A293659 * A293661 A293662 A293663

Keyword

nonn,base

Author

Felix Fröhlich, Dec 30 2017

Status

approved