A273007 a(n) is the smallest exponent > 1 such that p^a(n) ends with p, where p is the n-th prime.
5, 5, 2, 5, 11, 21, 21, 11, 21, 11, 11, 21, 6, 5, 21, 21, 11, 6, 21, 11, 21, 11, 21, 11, 21, 11, 101, 21, 51, 101, 101, 51, 101, 51, 11, 11, 21, 101, 101, 101, 51, 51, 51, 5, 101, 11, 51, 101, 101, 51, 101, 51, 26, 3, 21, 101, 51, 51, 101, 26, 101, 21, 5, 51
Offset: 1
Examples
2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32; 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 = 243.
Links
- Paolo P. Lava, Table of n, a(n) for n = 1..1000
Programs
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Maple
P:=proc(q) local d,k,n; for n from 1 to q do if isprime(n) then d:=ilog10(n)+1; for k from 2 to q do if n=(n^k mod 10^d) then print(k); break; fi; od; fi; od; end: P(10^3);
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Mathematica
Table[Length[NestWhileList[p #&,p^2,Mod[#,10^IntegerLength[p]]!=p&]]+1,{p,Prime[ Range[65]]}] (* Harvey P. Dale, Jul 25 2019 *)