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A230087 Primes such that prime plus its digit sum is a perfect square.

%I A230087 #30 Sep 08 2022 08:46:06
%S A230087 2,17,179,347,467,521,1433,1583,2111,3347,10601,12527,25889,28541,
%T A230087 32027,33113,39569,39971,41201,43661,45767,55667,58061,59513,61001,
%U A230087 62969,63977,67061,70199,77261,92387,92993,100469,109541,120401,122477,130307,156011,163193
%N A230087 Primes such that prime plus its digit sum is a perfect square.
%C A230087 Number of primes obtained from the sequence ‘prime plus its digit sum is perfect square’ is 150 for n = 1 to 3*10^5, while the sequence for ‘perfect cube’ yields only 11 primes for the same range of n. Hence, sequence for ‘square’ is framed.
%C A230087 Subsequence of primes of A066564. - _Michel Marcus_, Jun 02 2015
%H A230087 K. D. Bajpai and Charles R Greathouse IV, <a href="/A230087/b230087.txt">Table of n, a(n) for n = 1..10000</a> (terms 2..150 from Bajpai)
%e A230087 a(2) = 17 is prime. Digit sum of 17 = 8, 17 + 8 = 25 = 5^2.
%e A230087 a(5) = 467 is prime. Digit sum of 467 = 17, 467 + 17 = 484 = 22^2.
%p A230087 KD:= proc() local a,b,c,d; a:= ithprime(n);b:=add( i,i = convert((a), base, 10))(a); c:=a+b; d:=evalf(sqrt(c)); if d=floor(d) then return (a) :fi;end:seq(KD(),n=1..50000);
%o A230087 (PARI) for(n=2,1e4,forprime(p=n^2-9*#digits(n^2),n^2, if(p+sumdigits(p) == n^2, print1(p", ")))) \\ _Charles R Greathouse IV_, Oct 08 2013
%o A230087 (Magma) [p: p in PrimesUpTo(6*10^5) | IsSquare(p+(&+Intseq(p)))]; // _Vincenzo Librandi_, Jun 02 2015
%Y A230087 Cf. A048519.
%Y A230087 Cf. A107288 (Primes whose digit sum is square).
%K A230087 nonn,base,less
%O A230087 1,1
%A A230087 _K. D. Bajpai_, Oct 08 2013
%E A230087 a(1) from _Charles R Greathouse IV_, Oct 08 2013