A178659 -id:A178659 - cp's OEIS frontend

A178660 Numbers k such that k^3 +- (k+5)^2 are primes.

7, 12, 13, 18, 58, 142, 187, 502, 597, 657, 702, 907, 912, 942, 943, 972, 1057, 1168, 1248, 1357, 1453, 1533, 1663, 1938, 2013, 2088, 2272, 2373, 2478, 2608, 2848, 2968, 3003, 3028, 3108, 3247, 3423, 3478, 3583, 3817, 3927, 3957, 4132, 4212, 4632, 4668

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jun 01 2010

nonn

			7 is a term since: 7^3 +- 12^2 -> (199,487) which are primes.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A068501, A137475, A178659.

Select[Range[8! ],PrimeQ[ #^3-(#+5)^2]&&PrimeQ[ #^3+(#+5)^2]&]
Select[Range[4700],AllTrue[#^3+{(#+5)^2,-(#+5)^2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 19 2018 *)

A254886 a(n) = least k>0 such that n-k^2 and n+k^2 are both primes.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 2, 0, 2, 0, 0, 1, 0, 3, 2, 0, 0, 1, 0, 3, 4, 3, 0, 0, 0, 0, 2, 3, 0, 1, 0, 3, 2, 0, 0, 5, 0, 3, 0, 0, 0, 1, 6, 0, 4, 0, 6, 5, 0, 3, 0, 3, 6, 5, 0, 0, 2, 0, 0, 1, 0, 3, 2, 0, 6, 0, 6, 0, 0, 3, 0, 1, 6, 0, 2, 0, 6, 5, 0, 3, 0, 0, 0, 5, 0, 9, 4, 3, 0, 7, 0, 3, 2, 0, 6, 0, 0, 3, 0, 9, 0, 1, 6, 0, 2, 0, 0, 1, 0

Offset: 1

Zak Seidov, Feb 10 2015

nonn

If n is a square then a(n)=sqrt(n)-1 or 0.
Also if n is a square and a(n)=sqrt(n)-1 then sqrt(n) is a term in A178659.
First appearances of k for k=1..58 are at n = 4, 7, 14, 21, 36, 43, 90, 117, 86, 111, 210, 149, 768, 201, 236, 285, 468, 329, 366, 411, 446, 1137, 534, 647, 654, 807, 770, 885, 900, 911, 3090, 1665, 1192, 2415, 1296, 1313, 4212, 2163, 1600, 1671, 5448, 1769, 2040, 1941, 2054, 3207, 2214, 2333, 5340, 2601, 2792, 7725, 2814, 3095, 3054, 5913, 3442, 4377.
Among the first 10000 terms, the first missing values are 59, 79, 82, 83, 89, 91, 92, 94, 97, 98, 100.

Cf. A068501, A082467, A178659.

PARI
```
k=1;while(k^2Derek Orr, Feb 11 2015
```

cp's OEIS Frontend

A178660 Numbers k such that k^3 +- (k+5)^2 are primes.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica