login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A293660 Base-7 circular primes that are not base-7 repunits. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: The sequence is finite.

LINKS

Table of n, a(n) for n=1..51.

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

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 20 09:59 EDT 2019. Contains 322309 sequences. (Running on oeis4.)