A345903 - OEIS

A345903

The succession of prime and nonprime terms is kept when you consider the sequence formed by the successive sums a(n) + a(n+1). This is the lexicographically earliest sequence of distinct positive terms with this property.

2, 1, 3, 4, 5, 6, 8, 7, 10, 11, 12, 9, 13, 16, 14, 18, 15, 17, 20, 19, 22, 23, 24, 21, 25, 26, 28, 27, 29, 30, 32, 31, 36, 33, 35, 34, 38, 37, 42, 39, 41, 48, 40, 44, 43, 46, 45, 47, 50, 49, 51, 53, 54, 52, 56, 55, 57, 58, 59, 68, 60, 61, 66, 62, 63, 65, 64, 69, 67, 70

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..70.

FORMULA

a(n) = A345966(n) for n >= 7. - Pontus von Brömssen, Jul 03 2021

EXAMPLE

Here is the succession of primes and nonprimes in the sequence:

2, 1, 3, 4, 5, 6, 8, 7, 10, 11, 12, 9, 13, 16, 14, 18, 15, ...

p n p n p n n p n p n n p n n n n

The same succession is formed by a(n) + a(n+1):

3, 4, 7, 9, 11, 14, 15, 17, 21, 23, 21, 22, 29, 30, 32, 33, 32, ...

p n p n p n n p n p n n p n n n n

MATHEMATICA

seq[n_] := Module[{s = {2}, q, k}, Do[q = PrimeQ[s[[-1]]]; k = 1; While[!FreeQ[s, k] || PrimeQ[s[[-1]] + k] != q, k++]; AppendTo[s, k], {n}]; s]; seq[100] (* Amiram Eldar, Jul 02 2021 *)

CROSSREFS

Cf. A345966.

Sequence in context: A226054 A109920 A109919 * A346786 A239469 A282840

Adjacent sequences: A345900 A345901 A345902 * A345904 A345905 A345906

KEYWORD

nonn

AUTHOR

Eric Angelini and Carole Dubois, Jul 02 2021

STATUS

approved