A380669 Smallest prime p > 10^(n-1) for which successive cyclic shifts of digits by 1, ..., n-1 positions to the right are all prime, or -1 if no such p exists.

2, 11, 113, 1193, 11939, 193939, 93717773, 139133119, 15193739179, 153991739117, 877317793117

Offset

1,1

Comments

For n in A004023, a(n) = (10^n-1)/9. - Robert Israel, Feb 04 2025

Links

Table of n, a(n) for n=1..11.

Example

n p  shifts of digits by 1, ..., n-1 positions (n <= number of digits of p) to the right
1 2 -> ;
2 11 -> 11;
3 113 -> 311, 131;
4 1193 -> 3119, 9311, 1931;
5 11939 -> 91193, 39119, 93911, 19391;
6 193939 -> 919393, 391939, 939193, 393919, 939391;
7 93717773 -> 39371777, 73937177, 77393717, 77739371, 17773937, 71777393, but 37177739 = 29 * 683 * 1877;
8 139133119 -> 913913311, 191391331, 119139133, 311913913, 331191391, 133119139, 913311913, but 391331191 = 29 * 131 * 239 * 431;
9 15193739179 -> 91519373917, 79151937391, 17915193739, 91791519373, 39179151937, 73917915193, 37391791519, 93739179151, but 19373917915 = 5 * 11 * 29 * 823 * 14759;
10 153991739117 -> 715399173911, 171539917391, 117153991739, 911715399173, 391171539917, 739117153991, 173911715399, 917391171539, 991739117153, but 399173911715 = 5 * 79834782343;
11 877317793117 -> 787731779311, 178773177931, 117877317793, 311787731779, 931178773177, 793117877317, 779311787731, 177931178773, 317793117877, 731779311787, but 773177931178 = 2 * 386588965589;

Crossrefs

Cf. A004023, A247153, A380655.

Sequence in context: A069574 A090534 A380655 * A376447 A371697 A373795

Adjacent sequences: A380666 A380667 A380668 * A380670 A380671 A380672

Keyword

nonn,base,more

Author

Jean-Marc Rebert, Jan 30 2025

Extensions

a(9)-a(11) corrected by Pontus von Brömssen, Feb 24 2025

Status

approved