These two sequences of positive integers are defined as:
$$R(1)=1\ ;\ S(1)=2 \\R(n)=R(n-1)+S(n-1), \quad n>1.$$
The sequence $S(n)$ is further defined as the sequence of positive integers not present in $R(n)$.
Sequence $R$ starts:
1, 3, 7, 12, 18, ...
Sequence $S$ starts:
2, 4, 5, 6, 8, ...
Task: Create two functions named ffr and ffs that when given n return R(n) or S(n) respectively.(Note that R(1) = 1 and S(1) = 2 to avoid off-by-one errors). No maximum value for n should be assumed. Sloane's A005228 and A030124. Wolfram MathWorld Wikipedia: Hofstadter Figure-Figure sequences.ffr
is a function.
testString: assert(typeof ffr === 'function', 'ffr
is a function.');
- text: ffs
is a function.
testString: assert(typeof ffs === 'function', 'ffs
is a function.');
- text: ffr
should return integer.
testString: assert(Number.isInteger(ffr(1)), 'ffr
should return integer.');
- text: ffs
should return integer.
testString: assert(Number.isInteger(ffs(1)), 'ffs
should return integer.');
- text: ffr()
should return 69
testString: assert.equal(ffr(ffrParamRes[0][0]), ffrParamRes[0][1], 'ffr()
should return 69
');
- text: ffr()
should return 1509
testString: assert.equal(ffr(ffrParamRes[1][0]), ffrParamRes[1][1], 'ffr()
should return 1509
');
- text: ffr()
should return 5764
testString: assert.equal(ffr(ffrParamRes[2][0]), ffrParamRes[2][1], 'ffr()
should return 5764
');
- text: ffr()
should return 526334
testString: assert.equal(ffr(ffrParamRes[3][0]), ffrParamRes[3][1], 'ffr()
should return 526334
');
- text: ffs()
should return 14
testString: assert.equal(ffs(ffsParamRes[0][0]), ffsParamRes[0][1], 'ffs()
should return 14
');
- text: ffs()
should return 59
testString: assert.equal(ffs(ffsParamRes[1][0]), ffsParamRes[1][1], 'ffs()
should return 59
');
- text: ffs()
should return 112
testString: assert.equal(ffs(ffsParamRes[2][0]), ffsParamRes[2][1], 'ffs()
should return 112
');
- text: ffs()
should return 1041
testString: assert.equal(ffs(ffsParamRes[3][0]), ffsParamRes[3][1], 'ffs()
should return 1041
');
```