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
Keywords
Examples
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.
Links
- 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.
Crossrefs
Cf. A226484.
Programs
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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 *) -
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
Comments