A253917 Numbers that can be represented as both x^y + x and b^c + b + c, for some b, c, x, y > 1.

72, 738, 2758, 16777232, 1073741856, 282429536508, 95367431640650, 150094635296999148, 221073919720733357899812, 311973482284542371301330321821976098, 1329227995784915872903807060280344640, 85070591730234615865843651857942052992

Offset

1,1

Comments

Intersection of A253913 and A253775.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..17

Robert G. Wilson v, 51 identified terms with no assurance that these are the only terms less than 10^1000.

Example

72 = 2^6+2+6 = 8^2+8,
738 = 3^6+3+6 = 9^3+9,
2758 = 52^2+52+2 = 14^3+14,
16777232 = 4^12+4+12 = 8^8+8,
1073741856 = 2^30+2+30 = 32^6+32,
282429536508 = 3^24+3+24 = 27^8+27,
95367431640650 = 5^20+5+20 = 25^10+25,
150094635296999148 = 9^18+9+18 = 27^12+27,
221073919720733357899812 = 6^30+6+30 = 30^15+36,
311973482284542371301330321821976098 = 7^42+7+42 = 49^21+49,
1329227995784915872903807060280344640 = 4^60+4+60 = 64^20+64,
85070591730234615865843651857942052992 = 2^126+2+126 = 128^18+128,
etc. - Robert G. Wilson v, Jan 19 2015

Mathematica

f[n_] := Block[{t = Transpose@ Flatten[ Table[{m^k + m, m^k + m + k}, {m, 2, Floor@ Sqrt[2^n]}, {k, Floor@ Log[m, 2^(n - 1)] + 1, Floor@ Log[m, 2^n]}], 1]}, Intersection[ t[[1]], t[[2]]]]; f[1] = {}; Array[f, 50] // Flatten (* Robert G. Wilson v, Jan 19 2015 *)

Crossrefs

Cf. A253913, A253775, A253914, A253916.

Sequence in context: A077120 A200451 A097205 * A008448 A282213 A304828

Adjacent sequences: A253914 A253915 A253916 * A253918 A253919 A253920

Keyword

nonn,more

Author

Alex Ratushnyak, Jan 18 2015

Extensions

a(7)-a(12) from Robert G. Wilson v, Jan 19 2015

Status

approved