A225106 Prime powers (A025475) that can be represented as a sum of two distinct prime powers.

9, 25, 81, 125, 512, 5041

Offset: 1

Author

Alex Ratushnyak, Apr 28 2013

Keywords

• nonn
• hard
• more

Comments

The next term, if it exists, is bigger than 2^64.

Conjecture: the sequence is finite. - Alex Ratushnyak, Feb 03 2020

Examples

			9 = 8 + 1.
25 = 16 + 9.
81 = 32 + 49.
125 = 121 + 4.
512 = 169 + 343.
5041 = 128 + 4913.
		

Links

• Alex Ratushnyak, C program

Crossrefs

Cf. A025475, A331701.

Programs

C

/* See Ratushnyak link. */

Mathematica

nn = 10000; p = Sort[Flatten[Table[Prime[n]^i, {n, PrimePi[Sqrt[nn]]}, {i, 2, Log[Prime[n], nn]}]]]; p = Join[{1}, p]; t = Union[Select[Flatten[Table[p[[i]] + p[[j]], {i, Length[p] - 1}, {j, i + 1, Length[p]}]], # <= nn &]]; Intersection[p, t] (* T. D. Noe, Apr 29 2013 *)