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Numbers that are sums of consecutive powers of 3.
4

%I #10 Aug 19 2019 23:45:40

%S 1,3,4,9,12,13,27,36,39,40,81,108,117,120,121,243,324,351,360,363,364,

%T 729,972,1053,1080,1089,1092,1093,2187,2916,3159,3240,3267,3276,3279,

%U 3280,6561,8748,9477,9720,9801,9828,9837,9840,9841,19683,26244,28431

%N Numbers that are sums of consecutive powers of 3.

%C Numbers of the form (3^i - 3^j)/2 with i > j.

%H Robert Israel, <a href="/A309758/b309758.txt">Table of n, a(n) for n = 1..10000</a>

%e 1080 = 3^3 + 3^4 + 3^5 + 3^6, so 1080 is in the sequence.

%e +------+--------+

%e | a(n) | base 3*|

%e +------+--------+

%e | 1 | 1 |

%e | 3 | 10 |

%e | 4 | 11 |

%e | 9 | 100 |

%e | 12 | 110 |

%e | 13 | 111 |

%e | 27 | 1000 |

%e | 36 | 1100 |

%e | 39 | 1110 |

%e | 40 | 1111 |

%e +------+--------+

%e * - a(n) written in base 3.

%p [seq(seq((3^i-3^j)/2,j=i-1..0,-1),i=1..20)]; # _Robert Israel_, Aug 19 2019

%Y Cf. A000244, A005836, A023758, A038464, A309759, A309761.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Aug 15 2019