A293142 -id:A293142 - cp's OEIS frontend

A293663 Circular primes that are not repunits.

2, 3, 5, 7, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11939, 19391, 19937, 37199, 39119, 71993, 91193, 93719, 93911, 99371, 193939, 199933, 319993, 331999, 391939

Offset: 1

Felix Fröhlich, Dec 30 2017

Relative complement of A004022 in A068652.
Conjecture: The sequence is finite.
From Michael De Vlieger, Dec 30 2017: (Start)
Primes > 5 in this sequence must only have digits that are in the reduced residue system modulo 10, i.e., {1, 3, 7, 9}.
There are 54 terms that have 6 or fewer decimal digits, the largest of which is 999331.
a(55) must be larger than 10^11. (End) [Corrected by Felix Fröhlich, Mar 15 + 24 2019]
From Felix Fröhlich, Mar 16 2019: (Start)
a(55) > 10^23 if it exists (cf. De Geest link).
Numbers k such that A262988(k) = A055642(k). (End)

			The numbers resulting from cyclic permutations of the digits of 1193 are 1931, 9311 and 3119, respectively and all those numbers are prime, so 1193, 1931, 3119 and 9311 are terms of the sequence.

Felix Fröhlich, Table of n, a(n) for n = 1..54
P. De Geest, Circular Primes

Cf. A004022, A055642, A068652, A262988, A293142.

Cf. base-b nonrepunit circular primes: A293657 (b=4), A293658 (b=5), A293659 (b=6), A293660 (b=7), A293661 (b=8), A293662 (b=9).

Select[Prime@ Range[10^5], Function[w, And[AllTrue[Array[FromDigits@ RotateRight[w, #] &, Length@ w - 1], PrimeQ], Union@ w != {1} ]]@ IntegerDigits@ # &] (* or *)
Select[Flatten@ Array[FromDigits /@ Most@ Rest@ Tuples[{1, 3, 7, 9}, #] &, 9, 2], Function[w, And[AllTrue[Array[FromDigits@ RotateRight[w, #] &, Length@ w], PrimeQ], Union@ w != {1} ]]@ IntegerDigits@ # &] (* Michael De Vlieger, Dec 30 2017 *)

eva(n) = subst(Pol(n), x, 10)
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
is_circularprime(p) = my(d=digits(p), r=rot(d)); if(vecmin(d)==0, return(0), while(1, if(!ispseudoprime(eva(r)), return(0)); r=rot(r); if(r==d, return(1))))
forprime(p=1, , if(vecmax(digits(p)) > 1, if(is_circularprime(p), print1(p, ", "))))

/* The following is a much faster program that only tests numbers whose decimal expansion consists of digits from the set {1, 3, 7, 9}. */
eva(n) = subst(Pol(n), x, 10)
next_v(vec) = my(k=#vec); if(vecmin(vec)==9, vec=concat(vector(#vec, t, 1), [3]); return(vec)); while(k > 0, if(vec[k]==9, vec[k]=1, if(vec[k]==3, vec[k]=7; return(vec), vec[k]=vec[k]+2, return(vec))); k--)
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
search(n) = my(d=digits(n), e=[], ed=0); while(1, e=rot(d); while(1, if(!ispseudoprime(eva(e)), break, e=rot(e); if(e==d && ispseudoprime(eva(e)), print1(eva(d), ", "); break))); d=next_v(d))
searchfrom(n) = if(n < 12, forprime(p=n, 10, print1(p, ", ")); search(13), my(d=digits(n)); for(k=1, #d, if(d[k]%2==0, d[k]++, if(d[k]==5, d[k]=7))); search(eva(d)))
/* Start a search from 1 upwards as follows: */
searchfrom(1) \\ Felix Fröhlich, Mar 23 2019

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

Original entry on oeis.org

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

Felix Fröhlich, Dec 30 2017

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

			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.

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

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).

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 *)

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, ", "))))

A293657 Base-4 circular primes that are not base-4 repunits.

Original entry on oeis.org

7, 13, 23, 29, 53, 383, 509, 863, 983, 1013

Offset: 1

Felix Fröhlich, Oct 28 2017

Conjecture: The sequence is finite, with 1013 being the last term (see A293142).
Written in base 4 (A007090), the terms are 13, 31, 113, 131, 311, 11333, 13331, 31133, 33113, 33311. - Antti Karttunen, Nov 26 2017
From Michael De Vlieger, Dec 30 2017: (Start)
The digits of primes in this sequence must be in the reduced residue system modulo 4, i.e., {1, 3}.
a(11), if it exists, must be larger than 4^21 = 4398046511104. (End)

			53 written in base 4 is 311. The base-4 numbers 311, 131, 113 written in base 10 are 53, 29, 23, respectively and all those numbers are prime, so 23, 29 and 53 are terms of the sequence.

Cf. A007090, A293142.

Cf. base-b nonrepunit circular primes: A293658 (b=5), A293659 (b=6), A293660 (b=7), A293661 (b=8), A293662 (b=9), A293663 (b=10).

With[{b = 4}, Select[Array[Map[If[Union@ # == {1}, 0, FromDigits[#, b]] &, NestList[RotateLeft, #, Length@ # - 1]] &@ IntegerDigits[Prime@ #, b] &, 10^6, If[PrimeQ@ b, #, # + 1] &@ PrimePi@ b], AllTrue[#, PrimeQ] &][[All, 1]] ] (* Michael De Vlieger, Nov 26 2017 *)
With[{b = 4}, Select[Flatten@ Array[FromDigits[#, b] & /@ Most@ Rest@ Tuples[{1, 3}, #] &, 18, 2], Function[w, And[ AllTrue[ Array[ FromDigits[ RotateRight[w, #], b] &, Length@ w], PrimeQ], Union@ w != {1} ]]@ IntegerDigits[#, b] &]] (* Michael De Vlieger, Dec 30 2017 *)

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, 4))!=vecmax(digits(p, 4)), if(is_circularprime(p, 4), print1(p, ", "))))

A293658 Base-5 circular primes that are not base-5 repunits.

Original entry on oeis.org

7, 11, 13, 17, 19, 23, 167, 211, 239, 283, 359, 431, 547, 571, 1069, 1249, 1733, 2221, 2417, 2713, 2749, 3049, 3109, 3121

Offset: 1

Felix Fröhlich, Oct 28 2017

Conjecture: The sequence is finite, with 3121 being the last term (see A293142).
Written in base 5 (A007091), the terms are 12, 21, 23, 32, 34, 43, 1132, 1321, 1424, 2113, 2414, 3211, 4142, 4241, 13234, 14444, 23413, 32341, 34132, 41323, 41444, 44144, 44414, 44441. - Antti Karttunen, Nov 26 2017
a(25), if it exists, must be larger than prime(10^6) = 15485863, an 11-digit quinary number. - Michael De Vlieger, Nov 26 2017

			1069 written in base 5 is 13234. The base-5 numbers 13234, 32341, 23413, 34132, 41323 written in base 10 are 1069, 2221, 1733, 2417, 2713, respectively and all those numbers are prime, so 1069, 1733, 2221, 2417 and 2713 are terms of the sequence.

Cf. A007091, A293142.

Cf. base-b nonrepunit circular primes: A293657 (b=4), A293659 (b=6), A293660 (b=7), A293661 (b=8), A293662 (b=9), A293663 (b=10).

Select[Array[Map[If[Union@ # == {1}, 0, FromDigits[#, 5]] &, NestList[RotateLeft, #, Length@ # - 1]] &@ IntegerDigits[Prime@ #, 5] &, 10^5, 4], AllTrue[#, PrimeQ] &][[All, 1]] (* Michael De Vlieger, Nov 26 2017 *)

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, 5))!=vecmax(digits(p, 5)), if(is_circularprime(p, 5), print1(p, ", "))))

A293659 Base-6 circular primes that are not base-6 repunits.

Original entry on oeis.org

11, 31, 71, 191, 211

Offset: 1

Felix Fröhlich, Oct 28 2017

Conjecture: The sequence is finite, with 211 being the last term (see A293142).
Written in base 6 (A007092), the terms are 15, 51, 155, 515, 551. - Antti Karttunen, Nov 26 2017
From Michael De Vlieger, Dec 30 2017: (Start)
This sequence may be particularly constrained to few terms since only {1, 5} are coprime to 6, and any senary circular prime involves just these 2 senary digits. This is because all primes aside from {2, 3} are congruent to {1, 5} (mod 6). Since a senary number consisting of all 5's is divisible by 5 and since we have disqualified prime repunits, the sequence is probably finite.
a(6), if it exists, must be larger than 6^21 = 21936950640377856. (End)

			71 written in base 6 is 155. The base-6 numbers 155, 515, 551 written in base 10 are 71, 191, 211, respectively and all those numbers are prime, so 71, 191 and 211 are terms of the sequence.

Cf. A007092, A293142.

Cf. base-b nonrepunit circular primes: A293657 (b=4), A293658 (b=5), A293660 (b=7), A293661 (b=8), A293662 (b=9), A293663 (b=10).

With[{b = 6}, Select[Prime@ Range[PrimePi@ b + 1, 10^6], Function[w, And[AllTrue[Array[FromDigits[RotateRight[w, #], b] &, Length@ w - 1], PrimeQ], Union@ w != {1} ]]@ IntegerDigits[#, b] &]] (* or *)
With[{b = 6}, Select[Flatten@ Array[FromDigits[#, 6] & /@ Most@ Rest@ Tuples[{1, 5}, #] &, 18, 2], Function[w, And[ AllTrue[ Array[ FromDigits[ RotateRight[w, #], b] &, Length@ w], PrimeQ], Union@ w != {1} ]]@ IntegerDigits[#, b] &]] (* Michael De Vlieger, Dec 30 2017 *)

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, 6))!=vecmax(digits(p, 6)), if(is_circularprime(p, 6), print1(p, ", "))))

A293661 Base-8 circular primes that are not base-8 repunits.

Original entry on oeis.org

13, 29, 31, 41, 43, 47, 59, 61, 607, 719, 751, 761, 971, 1021, 1657, 1759, 1787, 1913, 1993, 2011, 2687, 3019, 3659, 3673, 3677, 3803, 3919, 4073, 49103, 56299, 62207, 105341, 130681, 177007, 188249, 195277, 235513, 237151, 251501, 259019, 4127707, 6807419

Offset: 1

Felix Fröhlich, Dec 30 2017

Conjecture: The sequence is finite.
From Michael De Vlieger, Dec 30 2017: (Start)
Primes in this sequence must only have odd digits.
There are 8 terms with 2 octal digits, 20 terms with 4 octal digits, 12 terms with 6 octal digits, and 8 terms with 8 octal digits.
a(49), if it exists, must be larger than 8^12 = 68719476736. (End)

			607 written in base 8 is 1137. The base-8 numbers 1137, 1371, 3711, 7113 written in base 10 are 607, 761, 1993, 3659, respectively, and all those numbers are prime, so 607, 761, 1993 and 3659 are terms of the sequence.

Cf. A007094, A293142.

Cf. base-b nonrepunit circular primes: A293657 (b=4), A293658 (b=5), A293659 (b=6), A293660 (b=7), A293662 (b=9), A293663 (b=10).

With[{b = 8}, Select[Prime@ Range[PrimePi@ b + 1, 10^6], Function[w, And[AllTrue[Array[FromDigits[RotateRight[w, #], b] &, Length@ w - 1], PrimeQ], Union@ w != {1} ]]@ IntegerDigits[#, b] &]] (* or *)
With[{b = 8}, Select[Flatten@ Array[FromDigits[#, b] & /@ Most@ Rest@ Tuples[Range[1, 7, 2], #] &, 6, 2], Function[w, And[ AllTrue[ Array[ FromDigits[ RotateRight[w, #], b] &, Length@ w], PrimeQ], Union@ w != {1} ]]@ IntegerDigits[#, b] &]] (* Michael De Vlieger, Dec 30 2017 *)

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, 8))!=vecmax(digits(p, 8)), if(is_circularprime(p, 8), print1(p, ", "))))

A293662 Base-9 circular primes that are not base-9 repunits.

Original entry on oeis.org

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

Felix Fröhlich, Dec 30 2017

Conjecture: The sequence is finite.

			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.

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).

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 *)

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, ", "))))

A317689 Largest nonrepunit base-n absolute prime (conjectured).

Original entry on oeis.org

7, 53, 3121, 211, 1999, 3803, 6469, 991, 161047, 19793, 16477, 24907, 683437, 3547, 67853, 80273, 94109, 72421

Offset: 3

Felix Fröhlich, Aug 04 2018

A base-b permutable or absolute prime is a prime p such that all numbers obtained from every permutation of the base-b digits of p and converted to base 10 are prime.

These primes were found using lim=10^8 in the PARI program and match those found with lim=10^5, lim=10^6 and lim=10^7. Therefore I conjecture that they are the correct values for those n.

Cf. A003459, A129338, A258706, A293142, A317688.

find_index_a(vec) = my(r=#vec-1); while(1, if(vec[r] < vec[r+1], return(r)); r--; if(r==0, return(-1)))
find_index_b(r, vec) = my(s=#vec); while(1, if(vec[r] < vec[s], return(s)); s--; if(s==r, return(-1)))
switch_elements(vec, firstpos, secondpos) = my(g); g=vec[secondpos]; vec[secondpos]=vec[firstpos]; vec[firstpos] = g; vec
reverse_order(vec, r) = my(v=[], w=[]); for(x=1, r, v=concat(v, vec[x])); for(y=r+1, #vec, w=concat(w, vec[y])); w=Vecrev(w); concat(v, w)
next_permutation(vec) = my(r=find_index_a(vec)); if(r==-1, return(0), my(s=find_index_b(r, vec)); vec=switch_elements(vec, r, s); vec=reverse_order(vec, r)); vec
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_absolute_prime(n, base) = my(db=vecsort(digits(n, base))); if(vecmin(db)==0 || vecmax(db)==1, return(0)); while(1, my(dec=decimal(db, base)); if(!ispseudoprime(dec), return(0)); db=next_permutation(db); if(db==0, return(1)))
a(n) = my(absp=0, lim=10^7, i=0); forprime(p=n+1, , if(is_absolute_prime(p, n), absp=p); i++; if(i==lim, return(absp)))

A326609 Largest minimal prime in base n (written in base 10).

Original entry on oeis.org

3, 13, 5, 3121, 5209, 2801, 76695841, 811, 66600049, 29156193474041220857161146715104735751776055777, 388177921

Offset: 2

Richard N. Smith, Jul 13 2019

a(13) is (probably) 13^32020*8+183, it has 35670 digits, a(14) = 14^85*4+65, it has 99 digits, a(15) = (15^106*66-619)/7, it has 126 digits, a(16) = 16^3544*9+145, it has 4269 digits.
a(17) is the smallest prime of the form (4105*17^k-9)/16 if it exists, otherwise (probably) (73*17^111333-9)/16 (136991 digits), a(18) = 18^31*304+1 (42 digits).
Other known terms: a(20) = (20^449*16-2809)/19 (585 digits), a(22) = 22^763*20+7041 (1026 digits), a(23) is (probably) (23^800873*106-7)/11 (1090573 digits), a(24) = (24^99*512-121)/23 (138 digits), a(30) = 30^1023*12+1 (1513 digits), a(42) = (42^487*27-1093)/41 (791 digits).
a(19) is the smallest prime of the form (15964*19^k-1)/3 if it exists, otherwise (probably) (904*19^110984-1)/3 (141924 digits), a(21) is the smallest prime of the form 16*21^k+335 if it exists, otherwise (probably) (51*21^479149-1243)/4 (633542 digits).

Richard N. Smith, Table of n, a(n) for n = 2..16
Curtis Bright, Raymond Devillers, and Jeffrey Shallit, Minimal Elements for the Prime Numbers, preprint, 2014.
Curtis Bright, Raymond Devillers, and Jeffrey Shallit, Minimal Elements for the Prime Numbers, Experimental Mathematics, Volume 25, 2016 - Issue 3.
C. K. Caldwell, The Prime Glossary, minimal prime
Richard N. Smith, List of all known terms
Top PRPs, Search for 8*13^n+183
Top PRPs, Search for (73*17^n-9)/16
Top PRPs, Search for (106*23^n-7)/11
Wikipedia, Minimal prime (recreational mathematics)

Cf. A071062 (base 10 minimal primes), A110600 (base 12 minimal primes).

Cf. A293142 (largest non-repunit permutable prime), A317689 (largest non-repunit circular prime), A103443 (largest left-truncatable prime), A023107 (largest right-truncatable prime), A323137 (largest two-sided prime), A084738 (smallest repunit prime), A186995 (smallest weakly prime).

A327811 Numbers obtained from cyclically permuting the base-7 digits of 13143449029 and converting back to decimal.

Original entry on oeis.org

2732225029, 4344971347, 5284288003, 6552690421, 7329791221, 8845405603, 8956420003, 9307441621, 9784676947, 9786942547, 13127589829, 13143449029

Offset: 1

Felix Fröhlich, Sep 26 2019

All terms are prime, therefore 13143449029 is a base-7 circular prime, see A293660.

13143449029 is remarkable in that it has 12 digits in base 7 and may be the largest known nonrepunit circular prime in that base.

			Base-7 expansion | Decimal value
---------------------------------
643464321244     | 13143449029
434643212446     |  8956420003
346432124464     |  7329791221
464321244643     |  9784676947
643212446434     | 13127589829
432124464346     |  8845405603
321244643464     |  6552690421
212446434643     |  4344971347
124464346432     |  2732225029
244643464321     |  5284288003
446434643212     |  9307441621
464346432124     |  9786942547

Cf. A293142, A293660, A327835.

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])
my(d=digits(13143449029, 7), e=d, v=[]); while(1, v=concat(v, [decimal(d, 7)]); d=rot(d); if(d==e, return(vecsort(v))))

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A293663 Circular primes that are not repunits.

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

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A293657 Base-4 circular primes that are not base-4 repunits.

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A293658 Base-5 circular primes that are not base-5 repunits.

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A293659 Base-6 circular primes that are not base-6 repunits.

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A293661 Base-8 circular primes that are not base-8 repunits.

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A293662 Base-9 circular primes that are not base-9 repunits.

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A317689 Largest nonrepunit base-n absolute prime (conjectured).

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