It appears to be consecutive prime numbers
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If you mean: 2 3 5 7 11 13 then they are all prime numbers
The pattern that occurs in the golden ratio is a spiral.
There is no number pattern in 781013. But there is a number pattern in the numbers 7, 8, 10, 13. 7+1=8 8+2=10 10+3=13 Can you see the pattern? And the next number in this sequence would be ... ?
The pattern is +5, -7... the answer is 6
If they are non-terminating and there is a repeating pattern, then they are rational. If they are non-terminating and there is no repeating pattern, as in pi, they are irrational.