Brian Beard - cp's OEIS frontend

User: Brian Beard

Brian Beard has authored 2 sequences.

A345668 Last prime minus distance to last prime.

1, 2, 1, 4, 3, 6, 5, 4, 3, 10, 9, 12, 11, 10, 9, 16, 15, 18, 17, 16, 15, 22, 21, 20, 19, 18, 17, 28, 27, 30, 29, 28, 27, 26, 25, 36, 35, 34, 33, 40, 39, 42, 41, 40, 39, 46, 45, 44, 43, 42, 41, 52, 51, 50, 49, 48, 47, 58, 57, 60, 59, 58, 57, 56, 55, 66, 65, 64

Offset: 3

Brian Beard, Jun 21 2021

nonn

Cf. A049711, A151799, A175856.

a[n_] := 2 * NextPrime[n, -1] - n; Array[a, 100, 3] (* Amiram Eldar, Jun 21 2021 *)

a(n) = p - (n-p) = 2*p - n where p is the largest prime < n.
a(n) = A151799(n) - A049711(n).
a(n) = A175856(n-1) - 1.

More terms from Jon E. Schoenfield, Jun 21 2021

A341130 a(n) = abs(a(n-1) - a(n-2)) if a(n-1) and a(n-2) are both prime or both composite. a(n) = a(n-1) + a(n-2) otherwise, where a(1) = 1 and a(2) = 2 and n > 2.

Original entry on oeis.org

1, 2, 3, 1, 4, 5, 9, 14, 5, 19, 14, 33, 19, 52, 71, 123, 194, 71, 265, 336, 71, 407, 478, 71, 549, 620, 71, 691, 620, 1311, 691, 2002, 2693, 4695, 7388, 2693, 10081, 12774, 2693, 15467, 12774, 28241, 15467, 43708, 59175, 15467, 74642, 90109, 15467, 105576, 121043

Offset: 1

Brian Beard, Feb 05 2021

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored logarithmic scatterplot of the first 2500 terms (where the color is function of the last prime number encountered) [A remarkable graph. - _N. J. A. Sloane_, Feb 13 2021]

Cf. A096062.

Block[{a = {1, 2}}, Do[AppendTo[a, Which[MemberQ[{##}, 1], Abs[#1 + #2], SameQ @@ PrimeQ[{##}], Abs[#1 - #2], True, Abs[#1 + #2]]] & @@ a[[-2 ;; -1]], {i, 49}]; a] (* Michael De Vlieger, Feb 05 2021 *)

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User: Brian Beard

A345668 Last prime minus distance to last prime.

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