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The HP-20S (F1890A) is an algebraic programmable scientific calculator produced by Hewlett-Packard from 1987 to 2000.. A member of HP's Pioneer series, the 20S was a low cost model targeted at students, using the same hardware as the HP-10B business calculator.
Up to 203 program steps are available, and up to 16 program/step labels. Each step and label uses one byte, which consumes register space in 7 byte increments. Here is a sample program that computes the factorial of an integer number from 2 to 69. The program takes up 9 bytes.
Here is a sample program that computes the factorial of an integer number from 2 to 69 (ignoring the calculator's built-in factorial/gamma function). There are two versions of the example: one for algebraic mode and one for RPN mode. The RPN version is significantly shorter. Algebraic version:
[10] [12] [13] The numbers of matchings in complete graphs, without constraining the matchings to be perfect, are instead given by the telephone numbers, which may be expressed as a summation involving double factorials. [14] Stirling permutations, permutations of the multiset of numbers 1, 1, 2, 2, ..., k, k in which each pair of equal numbers ...
Single-track Gray code: [63] each column is a cyclic shift of the other columns, plus any two consecutive permutations differ only in one or two transpositions. Nested swaps generating algorithm in steps connected to the nested subgroups +. Each permutation is obtained from the previous by a transposition multiplication to the left.
This is the limit of the probability that a randomly selected permutation of a large number of objects is a derangement. The probability converges to this limit extremely quickly as n increases, which is why !n is the nearest integer to n!/e. The above semi-log graph shows that the derangement graph lags the permutation graph by an almost ...
The TI-36X series is one of the few calculators [6] currently permitted for use on the Fundamentals of Engineering exam. While TI offers other calculators eligible for use on the exam, the TI-36X Pro is the most feature full Texas Instruments calculator permitted. HP and Casio also make calculators permitted on the exam.
Multiply together the results of the two previous steps The product of all primes up to n {\displaystyle n} is an O ( n ) {\displaystyle O(n)} -bit number, by the prime number theorem , so the time for the first step is O ( n log 2 n ) {\displaystyle O(n\log ^{2}n)} , with one logarithm coming from the divide and conquer and another coming ...