A228195 Primes with the property that the sum of the cubes of their digits plus the prime equals another prime squared.

17, 2897, 11471, 15527, 19949, 26693, 26783, 72467, 78041, 142757, 159209, 216791, 350747, 366917, 672593, 725891, 775007, 1187939, 1529153, 1659737, 2024093, 2035097, 2035349, 2105231, 2127761, 2598929, 2645933, 2917799, 3322439, 3497993, 3970643, 4042697, 4067513, 4280051, 4329257, 4464017, 5839397

Offset: 1

Author

Will Gosnell, Aug 15 2013

Keywords

• nonn
• base
• less

Examples

			17 is a term since (1^3 + 7^3) + 17 = 19^2.
2897 is a term since (2^3 + 8^3 + 9^3 + 7^3) + 2897 = 67^2.
11471 is a term since (1^3 + 1^3 + 4^3 + 7^3 + 1^3) + 11471 = 109^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Select[Prime[Range[403000]],PrimeQ[Sqrt[#+Total[IntegerDigits[#]^3]]]&] (* Harvey P. Dale, Oct 15 2023 *)

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

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)
v=[];for(n=1,9,v=concat(v,searchdigit(n))); v \\ Charles R Greathouse IV, Jun 16 2014

Extensions

a(10)-a(37) from Charles R Greathouse IV, Jun 16 2014