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A273527 a(n) is the smallest exponent > 1 such that p^a(n) begins with p, where p is the n-th prime.

%I A273527 #15 Jun 15 2016 09:41:28
%S A273527 8,18,24,20,26,10,166,19,48,14,58,45,205,31,248,30,49,178,3054,122,
%T A273527 140,294,174,80,152,233,79,920,295,359,107,308,257,8,180,96,98,34,230,
%U A273527 921,527,164,428,901,344,88,627,1003,192,240,50,38,1747,609,1028,432,122
%N A273527 a(n) is the smallest exponent > 1 such that p^a(n) begins with p, where p is the n-th prime.
%C A273527 Subset of A051248.
%H A273527 Harvey P. Dale, <a href="/A273527/b273527.txt">Table of n, a(n) for n = 1..200</a>
%F A273527 a(n) = A051248(A000040(n)).
%e A273527 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32, 2^6 = 64, 2^7 = 128, 2^8 = 256;
%e A273527 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 = 243, ..., 3^18 = 387420489.
%p A273527 P:=proc(q) local b,d,k,n; for n from 1 to q do if isprime(n) then d:=ilog10(n);
%p A273527 for k from 2 to q do b:=ilog10(n^k); if n=trunc(n^k/10^(b-d)) then print(k);
%p A273527 break; fi; od;  fi; od; end: P(10^6);
%t A273527 sep[n_]:=Module[{len=IntegerLength[n],idn=IntegerDigits[n],exp=2}, While[ Take[ IntegerDigits[ n^exp],len] != idn,exp++];exp]; sep/@Prime[ Range[ 60]] (* _Harvey P. Dale_, Jun 15 2016 *)
%Y A273527 Cf. A051248, A273007.
%K A273527 nonn,easy,base
%O A273527 1,1
%A A273527 _Paolo P. Lava_, May 24 2016