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%I #23 Oct 15 2023 16:47:29
%S 17,2897,11471,15527,19949,26693,26783,72467,78041,142757,159209,
%T 216791,350747,366917,672593,725891,775007,1187939,1529153,1659737,
%U 2024093,2035097,2035349,2105231,2127761,2598929,2645933,2917799,3322439,3497993,3970643,4042697,4067513,4280051,4329257,4464017,5839397
%N Primes with the property that the sum of the cubes of their digits plus the prime equals another prime squared.
%H Charles R Greathouse IV, <a href="/A228195/b228195.txt">Table of n, a(n) for n = 1..10000</a>
%e 17 is a term since (1^3 + 7^3) + 17 = 19^2.
%e 2897 is a term since (2^3 + 8^3 + 9^3 + 7^3) + 2897 = 67^2.
%e 11471 is a term since (1^3 + 1^3 + 4^3 + 7^3 + 1^3) + 11471 = 109^2.
%t Select[Prime[Range[403000]],PrimeQ[Sqrt[#+Total[IntegerDigits[#]^3]]]&] (* _Harvey P. Dale_, Oct 15 2023 *)
%o (PARI) is(n)=my(d=digits(n),k); issquare(sum(i=1,#d,d[i]^3)+n,&k) && isprime(k) && isprime(n) \\ _Charles R Greathouse IV_, Jun 16 2014
%o (PARI) searchdigit(n)=my(v=List(),N1=10^(n-1),N2=10^n,t=729*n,d,k,p2);forprime(p=sqrtint(N1)+1,sqrtint(N2+t),p2=p^2;forprime(q=max(N1,p2-t+2),min(N2,p2-2),d=digits(q);if(sum(i=1,#d,d[i]^3)+q==p2,listput(v,q))));Vec(v)
%o v=[];for(n=1,9,v=concat(v,searchdigit(n))); v \\ _Charles R Greathouse IV_, Jun 16 2014
%K nonn,base,less
%O 1,1
%A _Will Gosnell_, Aug 15 2013
%E a(10)-a(37) from _Charles R Greathouse IV_, Jun 16 2014
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