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

1,1

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A198594 A138199 A125000 * A032909 A367536 A239165

Adjacent sequences: A228192 A228193 A228194 * A228196 A228197 A228198

Keyword

nonn,base,less

Author

Will Gosnell, Aug 15 2013

Extensions

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

Status

approved