A230087 - OEIS

%I #30 Sep 08 2022 08:46:06

%S 2,17,179,347,467,521,1433,1583,2111,3347,10601,12527,25889,28541,

%T 32027,33113,39569,39971,41201,43661,45767,55667,58061,59513,61001,

%U 62969,63977,67061,70199,77261,92387,92993,100469,109541,120401,122477,130307,156011,163193

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

%C 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 Subsequence of primes of A066564. - _Michel Marcus_, Jun 02 2015

%H 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 a(2) = 17 is prime. Digit sum of 17 = 8, 17 + 8 = 25 = 5^2.

%e a(5) = 467 is prime. Digit sum of 467 = 17, 467 + 17 = 484 = 22^2.

%p 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 (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 (Magma) [p: p in PrimesUpTo(6*10^5) | IsSquare(p+(&+Intseq(p)))]; // _Vincenzo Librandi_, Jun 02 2015

%Y Cf. A048519.

%Y Cf. A107288 (Primes whose digit sum is square).

%K nonn,base,less

%O 1,1

%A _K. D. Bajpai_, Oct 08 2013

%E a(1) from _Charles R Greathouse IV_, Oct 08 2013