The ECG Sequence

In the ECG Sequence (that always starts with the numbers 1 and 2), every number that succeeds is the smallest not already present in the sequence and that shares a factor (excluding 1) with its preceding number. Every number in the ECG Sequence (besides 1 and 2) has a different index from its natural index in a normal numeric sequence. See the example below to establish the ECG Sequence Index of number 3.

// Find the smallest number that is not in sequence...
// This number shares a factor with the preceding?

SEQUENCE = [1, 2]

3 = no factors shared with 2
4 = shares factor 2 with number 2

SEQUENCE = [1, 2, 4]

3 = no factors shared with 4
5 = no factors shared with 4
6 = shares factor 2 with number 4

SEQUENCE = [1, 2, 4, 6]

3 = shares factor 3 with number 6

SEQUENCE = [1, 2, 4, 6, 3]

Number 3 is at index 4 in the ECG Sequence.

Given an integer n implement a function that returns its ECG Sequence Index.

Examples

ecgSeqIndex(3) ➞ 4

ecgSeqIndex(5) ➞ 9

ecgSeqIndex(7) ➞ 13

Notes

• ECG is the acronym for the electrocardiogram: if you try to graphically represent the trend of the sequence, a similar scheme appears.
• Curiosity: every odd prime p in the sequence is preceded by 2p and followed by 3p.