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%I #46 Nov 07 2021 17:19:32
%S 2,17,347,521,10601,28541,29759,32027,39569,58061,62969,100469,109541,
%T 120401,130307,205357,398129,426383,434261,829883,896771,923501,
%U 935063,1190261,1216583,1261109,1559963,1697771,2105381,2128649,2505857,2778851,2886563,2920649
%N Primes p such that p + digitsum(p) = q^k for some prime q and k > 1 where digitsum(n) = A007953(n).
%C With k>1 the number of entries is greatly reduced compared to simply allowing p+digsum(p) = q. One could allow for k=1 to see how many entries could be found for a variation of this sequence.
%H Kevin P. Thompson, <a href="/A242368/b242368.txt">Table of n, a(n) for n = 1..1000</a> (first 181 terms from Michel Marcus)
%e a(4)=521 because 521+5+2+1=529=23^2 and 23 is a prime.
%t a242368[n_Integer] := Module[{p, pp}, p = Prime[n]; pp = p + Plus @@ IntegerDigits@p; If[And[Length@FactorInteger[pp] == 1,
%t Min[Last@Transpose[FactorInteger[pp]]] > 1], p, 0]]; Rest@Sort@DeleteDuplicates[a242368 /@ Range[10^6]] (* _Michael De Vlieger_, Aug 16 2014 *)
%o (PARI) dsum(n)=n=digits(n); sum(i=1,#n,n[i])
%o is(p)=isprimepower(p+dsum(p))>1 && isprime(p)
%o forprime(p=2,1e9,if(is(p), print1(p", "))) \\ _Charles R Greathouse IV_, Aug 16 2014
%Y Cf. A000040, A007953, A007605, A000961.
%K nonn,base
%O 1,1
%A _J. M. Bergot_, Aug 16 2014
%E More terms from _Charles R Greathouse IV_, Aug 16 2014
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