cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A371155 a(n) depends on the primality of a(n-1) and parity of n (see Comments lines for definition).

Original entry on oeis.org

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

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Author

Bill McEachen, Mar 13 2024

Keywords

Comments

Initial term a(1)=1 and thereafter:
If n is even and a(n-1) is prime, then a(n) = least prime > a(n-1).
If n is even and a(n-1) is composite and a(n-2) is prime, then a(n) = 1 + greatest prime < a(n-2).
Otherwise, a(n) = a(n-1) + 1.
Every integer will be seen, with many seen twice. Largest first differences will be at prime gaps. Starting at 3, pairs of consecutive primes appear. Interestingly, the values seen once seem to correspond to A093513 except for 2.

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.
		

Crossrefs

Cf. A093513.

Programs

  • 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 *)
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