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A273007 a(n) is the smallest exponent > 1 such that p^a(n) ends with p, where p is the n-th prime.

%I A273007 #34 Jul 25 2019 18:11:28
%S A273007 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,
%T A273007 11,101,21,51,101,101,51,101,51,11,11,21,101,101,101,51,51,51,5,101,
%U A273007 11,51,101,101,51,101,51,26,3,21,101,51,51,101,26,101,21,5,51
%N A273007 a(n) is the smallest exponent > 1 such that p^a(n) ends with p, where p is the n-th prime.
%H A273007 Paolo P. Lava, <a href="/A273007/b273007.txt">Table of n, a(n) for n = 1..1000</a>
%e A273007 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32;
%e A273007 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 = 243.
%p A273007 P:=proc(q) local d,k,n; for n from 1 to q do if isprime(n) then d:=ilog10(n)+1;
%p A273007 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);
%t A273007 Table[Length[NestWhileList[p #&,p^2,Mod[#,10^IntegerLength[p]]!=p&]]+1,{p,Prime[ Range[65]]}] (* _Harvey P. Dale_, Jul 25 2019 *)
%Y A273007 Cf. A051248, A115739, A273527.
%K A273007 nonn,easy,base
%O A273007 1,1
%A A273007 _Paolo P. Lava_, May 24 2016