A sequence of squares: n to the nth power
256
3125, 46656 This is the sequence I used: * 1 = 11 * 4 = 22 * 27 = 33 * 256 = 44 * 3125 = 55 * 46,656 = 66 * and so on...
46656 as it is 6 to the power of 6. Each in turn is the result of a number to the power of itself.
823,543 The pattern is n to the nth power.
The number is 27. (33) The sequence shows the lowest 7 nonzero values for the exponential series nn, i.e. 1 to the first power, 2 to the 2nd power, up to 7 to the 7th power. 1*1=1 2*2=4 3*3*3=27 4*4*4*4=256 5*5*5*5*5=3125 6*6*6*6*6*6=46656 7*7*7*7*7*7*7=823543
256
3125, 46656 This is the sequence I used: * 1 = 11 * 4 = 22 * 27 = 33 * 256 = 44 * 3125 = 55 * 46,656 = 66 * and so on...
int main (void) { puts ("1 4 27 256 3125"); return 0; }
46656 as it is 6 to the power of 6. Each in turn is the result of a number to the power of itself.
44 = 256
The pattern in the sequence 1, 4, 27, 256 is based on powers of integers: (1 = 1^1), (4 = 2^2), (27 = 3^3), and (256 = 4^4). Each term corresponds to the cube of its position in the sequence, where (n^n) represents the (n)-th term. Thus, the next number in the sequence would be (5^5 = 3125).
11 = 1 22 = 4 33 = 27 44 = 256 55 = 3125
27
312511 = 122 = 433 = 2744 = 25655 = 3125
823,543 The pattern is n to the nth power.
The series consists of numbers that can be expressed as powers of integers: (1 = 1^1), (4 = 2^2), (27 = 3^3), (X = 4^4), and (3125 = 5^5). Therefore, the missing number (X) is (4^4), which equals (256). Thus, the missing number in the series is (256).
The number is 27. (33) The sequence shows the lowest 7 nonzero values for the exponential series nn, i.e. 1 to the first power, 2 to the 2nd power, up to 7 to the 7th power. 1*1=1 2*2=4 3*3*3=27 4*4*4*4=256 5*5*5*5*5=3125 6*6*6*6*6*6=46656 7*7*7*7*7*7*7=823543