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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.

%I A380669 #29 Feb 25 2025 11:26:39
%S A380669 2,11,113,1193,11939,193939,93717773,139133119,15193739179,
%T A380669 153991739117,877317793117
%N 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.
%C A380669 For n in A004023, a(n) = (10^n-1)/9. - _Robert Israel_, Feb 04 2025
%e A380669 n p  shifts of digits by 1, ..., n-1 positions (n <= number of digits of p) to the right
%e A380669 1 2 -> ;
%e A380669 2 11 -> 11;
%e A380669 3 113 -> 311, 131;
%e A380669 4 1193 -> 3119, 9311, 1931;
%e A380669 5 11939 -> 91193, 39119, 93911, 19391;
%e A380669 6 193939 -> 919393, 391939, 939193, 393919, 939391;
%e A380669 7 93717773 -> 39371777, 73937177, 77393717, 77739371, 17773937, 71777393, but 37177739 = 29 * 683 * 1877;
%e A380669 8 139133119 -> 913913311, 191391331, 119139133, 311913913, 331191391, 133119139, 913311913, but 391331191 = 29 * 131 * 239 * 431;
%e A380669 9 15193739179 -> 91519373917, 79151937391, 17915193739, 91791519373, 39179151937, 73917915193, 37391791519, 93739179151, but 19373917915 = 5 * 11 * 29 * 823 * 14759;
%e A380669 10 153991739117 -> 715399173911, 171539917391, 117153991739, 911715399173, 391171539917, 739117153991, 173911715399, 917391171539, 991739117153, but 399173911715 = 5 * 79834782343;
%e A380669 11 877317793117 -> 787731779311, 178773177931, 117877317793, 311787731779, 931178773177, 793117877317, 779311787731, 177931178773, 317793117877, 731779311787, but 773177931178 = 2 * 386588965589;
%Y A380669 Cf. A004023, A247153, A380655.
%K A380669 nonn,base,more
%O A380669 1,1
%A A380669 _Jean-Marc Rebert_, Jan 30 2025
%E A380669 a(9)-a(11) corrected by _Pontus von Brömssen_, Feb 24 2025