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A226537 Numbers not of the form p + q^2 + r^3 + s^4 where p, q, r, and s are prime. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A004441 A004438 A109425 * A153679 A273887 A194906

Adjacent sequences:  A226534 A226535 A226536 * A226538 A226539 A226540

KEYWORD

nonn

AUTHOR

Jud McCranie, Jun 10 2013

STATUS

approved

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Last modified March 24 12:14 EDT 2019. Contains 321448 sequences. (Running on oeis4.)