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Prime numbers whose digit reversal is a powerful(1) number (A001694).
1

%I #21 Sep 14 2024 11:43:21

%S 23,61,163,293,487,521,691,821,1297,1861,2531,2731,4201,4441,4483,

%T 5209,5227,8429,8867,9049,9631,12391,14437,16141,16987,25153,25703,

%U 29741,52163,61483,63211,65579,65707,65899,67057,67901,69481,80687

%N Prime numbers whose digit reversal is a powerful(1) number (A001694).

%H Chai Wah Wu, <a href="/A115685/b115685.txt">Table of n, a(n) for n = 1..8201</a> (terms 1..458 from Robert Israel)

%e 8867 is prime and 7688 = 2^3 * 31^2.

%p N:= 10000; # to get all entries <= N

%p F:= proc(p)

%p local L,i,q,f;

%p if not isprime(p) then return false end if;

%p L:= convert(p,base,10);

%p q:= add(10^(i-1)*L[-i],i=1..nops(L));

%p f:= ifactors(q)[2];

%p not has(map2(op,2,f),1);

%p end proc;

%p select(F,[2*i+1 $ i=1..floor((N-1)/2)]);

%p # _Robert Israel_, Feb 11 2013

%t fQ[n_] := Min[ Last@# & /@ FactorInteger@ FromDigits@ Reverse@ IntegerDigits@ n] > 1; Select[ Prime@ Range@ 8000, fQ] (* _Robert G. Wilson v_, Feb 11 2013 *)

%Y Cf. A001694.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Jan 31 2006