A226537 Numbers not of the form p + q^2 + r^3 + s^4 where p, q, r, and s are prime.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 34, 37, 42, 43, 48, 53, 61, 67, 77, 82, 208

Offset

1,2

Comments

Probably finite.

There are no more terms < 10^11. - _Giovanni Resta_, Jun 10 2013

Links

Table of n, a(n) for n=1..41.

Liqun Hu and Li Yang, On pairs of equations in unlike powers of primes and powers of 2, Open Mathematics 15:1 (2017), 8 pp.

Example

31 = 3 + 2^2 + 2^3 + 2^4 so 31 is not in the sequence. 32 cannot be written in a similar way so it is in the sequence.

Mathematica

max = 300; pqrs1234 = Sort[Flatten[Table[Prime[p] + Prime[q]^2 + Prime[r]^3 + Prime[s]^4, {p, PrimePi[max]}, {q, PrimePi[Sqrt[max]]}, {r, PrimePi[max^(1/3)]}, {s, PrimePi[max^(1/4)]}]]]; Complement[Range[max], pqrs1234] (* _Alonso del Arte_, Nov 24 2013 *)

Prog

(PARI) is(n)=if(n<30, return(n>0)); forprime(s=2, sqrtnint(n-14, 4), my(lr=n-s^4); forprime(r=2, sqrtnint(lr-6, 3), my(lq=lr-r^3); forprime(q=2, sqrtint(lq-2), if(isprime(lq-q^2), return(0))))); 1 \\ _Charles R Greathouse IV_, Nov 13 2018

Crossrefs

Cf. A226484.

Sequence in context: A004438 A109425 A357873 * A349294 A153679 A273887

Adjacent sequences: A226534 A226535 A226536 * A226538 A226539 A226540

Keyword

nonn

Author

_Jud McCranie_, Jun 10 2013

Status

approved