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

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

Offset: 1

Author

Felix Fröhlich, Sep 26 2019

Keywords

• nonn
• base
• easy
• fini
• full

Comments

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.

Examples

			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
		

Crossrefs

Cf. A293142, A293660, A327835.

Programs

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])
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))))