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A226537
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Numbers not of the form p + q^2 + r^3 + s^4 where p, q, r, and s are prime.
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0
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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
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OFFSET
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1,2
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COMMENTS
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Probably finite.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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