Runsums Calculator (version 2) EXAMPLES

KEY to the examples on this page:

Input

[ ] indicates a box in the calculator for you to enter a number.
Numbers must be whole numbers bigger than 0.

Choices

Select your choice from a pull-down menu. In the examples here, the one picked in shown like this.

Buttons

(text) indicates a button to press after you have entered your numbers.

Results

All results are reported in the RESULTS box at the bottom of the Calculator page. You can cut text from this box to use elsewhere. There is also a button above the results area to clear its contents.
On this page, Results are shown like this.

Notation

A Runsum is indicated by two dots, e.g. 2+3+4+5=14 is written as 2..5=14. Note that 14 is itself a run of a single number.

Find the sum of a run

(Find the sum) of all the whole numbers from [3] to [6]

Computes 3+4+5+6 which is 18. The answer is reported in the RESULTS box:
The sum of all numbers from 3 to 6 is 18

Find runs with a given sum

(Find) a run that starts at [9] with a sum of [30]

Is there a number E for which 9..E=30? Yes:
The sum of the run from 9 to 11 is 30

(Find) a run that starts at [9] with a sum of [60]

Is there a number E for which 9..E=60? No:
There is no end number for a run starting at 9 with a sum of 60

(Find) a run that ends at [9] with a sum of [30]

Is there a number S to start a run S..9 with a sum of 30? Yes:
The sum of the run from 6 to 9 is 30

(Show) runs with a sum of [30]

30 has 4 runsums: 4..8=6..9=9..11=30

(Show) runs with a sum of [30] up to [32]

30 has 4 runsums: 4..8=6..9=9..11=30
31 has 2 runsums: 15..16=31
32 has 1 runsum: 32

(Count) runs with a sum of [105]

How many runsums are there for 105?
105 has 8 runsums

Find numbers with a certain number of runsums

(Find numbers) between [50] and [100] with exactly [4] runsums

Find numbers which have just 4 runsums. Report only those found in the range 50 to 100: Numbers in the range 50 to 100 with 4 runsums:
51,54,55,57,60,65,66,69,70,77,78,84,85,87,91,93,95

(Find the smallest number) with [4] runsums

The smallest number with 4 runsums is 15 = 3 x 5

(Find the smallest number) with [37] runsums

The "smallest numbers" have been pre-calculated for 1 to 1499 runsums. Sometimes these are too big to be displayed as an integer, in which case only its factors are shown:
The smallest number with 37 runsums is 3^36

Friends and Neighbours

(Show Friends a..b=b..c) with b=[9]

There are two Friends, one for 30 and one for 42:
b=9: 6..9=9..11=30; 3..9=9..12=42;

(Show Friends a..b=b..c) with b= [7]

There are no runsums of the same total that share 7:
b=7:

(Show Neighbours a..b=(b+1)..c) with b from [12] to [14]

There are 2 numbers (42 and 75) with neighbouring runsums for b=12, none for b=13 and one for b=14:
b=12: 9..12=13..15=42; 3..12=13..17=75;
b=13:
b=14: 1..14=15..20=105;

Triangular Numbers

(Show the triangle numbers) T([1]) up to t([4])

What are the first 4 triangle numbers?
T(1)=1
T(2)=3
T(3)=6
T(4)=10

(Show the triangle numbers near) [1000]

Triangle numbers near 1000
T(43)=946
T(44)=990
T(45)=1035
T(46)=1081

How does the calculator work?