A078413 - OEIS

%I #18 Jan 26 2019 11:08:59

%S 2,2,5,13,18,89,243,475,1257

%N Smallest positive integer than cannot be obtained from exactly n copies of n using parentheses and the operations +, -, /, *, ^ and concatenation.

%C a(7) >= 192. - _Rick L. Shepherd_, May 08 2003

%C From _Lars Blomberg_, Apr 08 2018: (Start)

%C The terms a(6)-a(9) have been computed with these rules:

%C Division by 0 or exponentiation 0^0 is not allowed.

%C Concatenation where at least one operand is a fraction or where the second operand is negative are skipped.

%C Exponentiations yielding > 100000 digits or with exponent > 32-bit signed integer are skipped. (End)

%H <a href="/index/Fo#4x4">Index entries for similar sequences</a>

%e With three 3's one can form 1=(3/3)^3, 2=3-3/3, 3=3+3-3, 4=3+3/3, but not 5, so a(3)=5.

%e With four 4's one can get 1=44/44, 2=4/4+4/4, 3=4-(4/4)^4, 4=4+(4-4)^4, 5=4+(4/4)^4, 6=(4+4)/4+4, 7=44/4-4, 8=4+4+4-4, 9=4+4+4/4, 10=(44-4)/4, 11=(4/4) | (4/4), 12=(44+4)/4, but not 13, so a(4)=13 (| denotes concatenation).

%e With five 5's one can get 1 = (((5 | 5) | 5)^(5 - 5)), 2 = (((5 | 5) - 5) / (5 * 5)), 3 = (((5 * 5) + 5) / (5 + 5)), 4 = (((5 / 5) * 5) - (5 / 5)), 5 = (((5 | 5) * 5) / (5 | 5)), 6 = (((5 | 5) + 5) / (5 + 5)),

%e 7 = (((5 / 5) + 5) + (5 / 5)), 8 = (( 5 + 5) - ((5 + 5) / 5)), 9 = (( 5 + 5) - ((5 / 5)^5)), 10 = (((5 | 5) / 5) - (5 / 5)), 11 = (((5 | 5) / 5)^(5 / 5)), 12 = (((5 | 5) / 5) + (5 / 5)),

%e 13 = (((5 | 5) + (5 + 5)) / 5), 14 = (((5 / 5) | 5) - (5 / 5)), 15 = (((5 / 5) | 5)^(5 / 5)), 16 = (((5 / 5) | 5) + (5 / 5)), 17 = (( 5 | (5^5)) / (5^5)), but not 18, so a(5) = 18.

%Y Cf. A078405.

%K nonn,base,more

%O 1,1

%A _N. J. A. Sloane_, Dec 28 2002

%E a(5) from _Frank Ellermann_, Dec 30 2002, who finds that a(6) >= 89

%E a(6)-a(9) from _Lars Blomberg_, Apr 08 2018