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a(1) = 0 since starting at 1 and ending at 1 is no transitions at all. - Rémi Guillaume, Dec 29 2023

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Cf. Same parity: A010051, A061007, A035026, A069754, A071574.

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Rémi Guillaume: Thank you all for your changes and answers.
In the second twin formula, «When n is composite» should be replaced with «When n is nonprime»; shouldn't it?
@Kevin Ryde:
● In my comment, why have you replaced «transition» with «transitions», please?
● Since you have moved my comment down, the upper comment looks as if I had signed it together with the lower comment; doesn't it?
● If: «a(1) = 0 since starting at 1 and ending at 1 is no transition at all»,
then an extra 0 term could possibly be added at the start of the present sequence:
«a(0) = 0 since starting at 0 and ending at 0 is no transition at all».
But if: «a(1) = 0 since starting at 0 and ending at 1 is no transition»,
then an extra 0 term could hardly be added at the start of the present sequence:
«a(0) = 0 since starting at -1 and ending at 0 is no transition»
would be «excessive», wouldn't it?
I need this point to be clarified, before I can point out something more general.

Rémi Guillaume: @Kevin Ryde: I'm sorry, I meant:
● In my example, why have you replaced «transition» with «transitions», please?
● Since you have moved my example down, the upper example looks as if I had signed it together with the lower example; doesn't it?

Kevin Ryde: A "-" style signature applies to the line (paragraph) it appears on.  it's usual and correct for the unsigned work of the original author to be follows by additional signed work of later contributors.

Kevin Ryde: I interpret transition to mean going from x to x+1.  Assuming the starting point is indeed intended to be 1, then for example a(2) considers a single transition 1 to 2, and finds that yes that's a change of primality, so count it.

Rémi Guillaume: ● In the second twin formula, «When n is composite» should be replaced with «When n is nonprime»; shouldn't it?
● Would it be reasonable to write the following comment (not example):
«An extra term, a(0) = 0, could possibly be added at the start of the sequence (since starting at 0 and ending at 0 would be no transition at all).»?
(I need this point to be clarified, before I can point out something more general.)
@Kevin Ryde:
Thank you for your answers.
In my example, why have you replaced «transition» with «transitions», please?

Kevin Ryde: Usually plural "transitions" for 0 things in English (when it arises, which tends to be in mathematics rather than real life :).

Kevin Ryde: "a(0) = 0, could possibly be added" would be discouraged, unless there's some great controversy about initial term.  If it was good, then would do it, instead of saying what might be done.  In this case, I don't think it's important and may as well leave it.

Rémi Guillaume: ● In the second twin formula, «When n is composite» should be replaced with «When n is nonprime»; shouldn't it?
● The remaining comment (not example) should be clarified «into» something like:
«The following sequences all appear to have the same parity (with[out] the extra zero term at the start of A010051 [and A069754]): A010051, A061007, A035026, A069754, A071574.»,
shouldn't it?

Rémi Guillaume: ● In the second twin formula, «When n is composite» should be rectified to «When n is nonprime»; shouldn't it??
● The remaining comment (not example) should be clarified to something like:
«The following sequences all appear to have the same parity (without the extra zero term at the start of A010051 and A069754): A010051, A061007, A035026, A069754, A071574.»,
shouldn't it?

a(1) = 0 since going from 1 (nonprime) to 1 (nonprime) is not a transition. - Rémi Guillaume, Dec 29 2023

a(1) = 0 since starting at 1 and ending at 1 is no transitions at all. - Rémi Guillaume, Dec 29 2023

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Kevin Ryde: 1 to 1 is not a transition.  It's not actually clear in the definition whether the starting point for transitioning was to be 1 or 0.  Doesn't change the result of course.

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a(6)=) = 4 because there are 4 transitions: 1 to 2, 3 to 4, 4 to 5 and 5 to 6.

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