A196520
Smallest Friedman number of order n.
Original entry on oeis.org
25, 279936, 31381059609, 1125899906842624, 1152921504606846976, 4722366482869645213696, 42391158275216203514294433201, 324518553658426726783156020576256
Offset: 1
Since 25 is the smallest Friedman number, it is the smallest Friedman number of order 1.
279936 = 6^7 = (9 - 3)^(9 - 2), together using the digits of the number itself. Hence it is the smallest Friedman number of order 2.
31381059609 = 9^11 = 9^(5+6) = 3^(30-8+0), together using the digits of the number itself. Hence it is the smallest Friedman number of order 3.
A218539
Numbers that are equal to the sum of the uniform platonic polyhedral (figurate) numbers (tetrahedral, cubic, octahedral, dodecahedral, or icosahedral) on each of their digits.
Original entry on oeis.org
0, 1, 20, 21, 24, 153, 240, 241, 289, 304, 324, 370, 371, 407, 440, 441, 593, 739, 2167, 2284, 2348, 2484, 2583, 2860, 2861, 3009, 3029, 3093, 3249, 4288, 5859, 6888, 7996, 9898
Offset: 1
The octahedral numbers are represented by the formula, y(x)=(2x^3+x)/3; apply this formula to each of the digits in a(18)=739, i.e., y(7)=231, y(3)=19, y(9)=489; sum=739; the dodecahedral numbers are represented by the formula, y(x)=x(3x-1)(3x-2)/2; apply this formula to each of the digits in a(34)=9898, i.e., y(9)=2725, y(8)=2024; y(9)=2725, y(8)=2024; sum=9898.
A280390
Integers that can be written using their individual decimal digits and the operations + - * / ^ but not the concatenation of their digits.
Original entry on oeis.org
25, 125, 127, 128, 216, 289, 343, 347, 625, 736, 1285, 1296, 1792, 2048, 2187
Offset: 1
125 is in the sequence since 5^(1+2) but 121 is not in the sequence. We do not accept 11^2 since 11 is the concatenation of two digits.
-
ops = {Plus, Subtract, Times, Divide, Power}; fQ[n_] := Length@ Select[ Groupings[ Permutations@ IntegerDigits@ n, ops -> 2], # == n &] > 0; k = 1; lst = {}; While[k < 1001, If[fQ@k, AppendTo[lst, k]]; k++]; lst (* requires Mathematica version 11 or better *)
Comments