A371155 a(n) depends on the primality of a(n-1) and parity of n (see Comments lines for definition).
1, 2, 3, 5, 6, 4, 5, 7, 8, 6, 7, 11, 12, 8, 9, 10, 11, 13, 14, 12, 13, 17, 18, 14, 15, 16, 17, 19, 20, 18, 19, 23, 24, 20, 21, 22, 23, 29, 30, 24, 25, 26, 27, 28, 29, 31, 32, 30, 31, 37, 38, 32, 33, 34, 35, 36, 37, 41, 42, 38, 39, 40, 41, 43, 44, 42, 43, 47
Offset: 1
Examples
From 2 we move to 3, it is prime, so go to 5. Next evaluation to 6, having departed from a prime, so go to 3 + 1 = 4. Next eval move to 5, it is prime, so go to 7. Next eval to 8, having departed from a prime, so go to 5 + 1 = 6. Next eval move to 7, it is prime, so go to 11. Next eval move to 12, having departed from a prime, so go to 7 + 1 = 8. Next eval move to 9. Next eval move to 10. Next eval move to 11, it is prime, so go to 13. This example adds the terms 3, 5, 6, 4, 5, 7, 8, 6, 7, 11, 12, 8, 9, 10, 11, 13.
Links
- Bill McEachen, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A093513.
Programs
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Mathematica
a[1] = 1; a[n_] := a[n] = If[EvenQ[n], If[PrimeQ[a[n-1]], NextPrime[a[n-1] + 1], If[CompositeQ[a[n-1]] && PrimeQ[a[n-2]], 1 + NextPrime[a[n-2], -1], a[n-1] + 1]], a[n-1] + 1]; Array[a, 100] (* Amiram Eldar, Mar 19 2024 *)
Comments