A225106 - OEIS

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A225106

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

9, 25, 81, 125, 512, 5041

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OFFSET

1,1

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..6.

Alex Ratushnyak, C program

EXAMPLE

9 = 8 + 1.

25 = 16 + 9.

81 = 32 + 49.

125 = 121 + 4.

512 = 169 + 343.

5041 = 128 + 4913.

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 *)

PROG

CROSSREFS

Cf. A025475, A331701.

Sequence in context: A166103 A327989 A192618 * A110970 A322939 A141583

Adjacent sequences: A225103 A225104 A225105 * A225107 A225108 A225109

KEYWORD

nonn,hard,more

AUTHOR

Alex Ratushnyak, Apr 28 2013

STATUS

approved