A129830 Conjectured first occurrence of numbers n with the property that there exist two consecutive primes p and q such that pq + n is a fourth power.

1, 4, 9, 10, 25, 35, 36, 46, 49, 64, 66, 75, 113, 144, 149, 179, 188, 196, 203, 221, 241, 250, 290, 302, 380, 395, 397, 400

Offset

1,2

Comments

It remains to prove that for certain n, pq+n != y^4 for all consecutive primes p and q. This list was computed for p and q with prime indices up to 10000.

Links

Table of n, a(n) for n=1..28.

Example

p=7,q=11,k=4. 7*11+4 = 81 = 3^4.

Prog

(PARI) primefourth(n, m) = { local(c, k, x, p1, p2, j); c=0; for(k=1, m, for(x=1, n, p1=prime(x); p2=(prime(x+1)); y=p1*p2+k; if(isfourth(y), c++; print1(k", "); break; ) ) ); c; } isfourth(n) = \Return 1 if n is a fourth power { local(r); r = sqrt(sqrt(n)); if(floor(r+.5)^4== n, 1, 0) }

Crossrefs

Cf. A129783.

Sequence in context: A332449 A191905 A113432 * A113434 A236024 A141395

Adjacent sequences: A129827 A129828 A129829 * A129831 A129832 A129833

Keyword

easy,nonn

Author

Cino Hilliard, May 21 2007

Status

approved