A280268 Numbers k such that Pell(k) and Pell(k+1) have the same prime signature where Pell(k) = A000129(k).

2, 14, 26, 38, 86, 94, 106, 214, 218, 334, 338, 381, 590, 605

Offset

1,1

Comments

Initial terms are 2, 2*7, 2*13, 2*19, 2*43, 2*47, 2*53, 2*107, 2*109.

Links

Table of n, a(n) for n=1..14.

Index to sequences related to prime signature.

Example

14 is a term because A000129(14) = 2 * 13^2 * 239 and A000129(15) = 5^2 * 29 * 269.

Mathematica

psig[n_]:=Sort[FactorInteger[n][[;; , 2]]]; Drop[With[{nn=220}, SequencePosition[psig/@ LinearRecurrence[ {2, 1}, {0, 1}, nn], {x_, x_}]][[;; , 1]]-1, 2] (* The program generates the first 9 terms of the sequence. *) (* Harvey P. Dale, Jul 07 2024 *)

Prog

(PARI) Pell(n) = ([2, 1; 1, 0]^n)[2, 1];
is(n) = vecsort(factor(Pell(n))[, 2]) == vecsort(factor(Pell(n+1))[, 2]);

Crossrefs

Cf. A000129, A100484.

Sequence in context: A051222 A194411 A017545 * A109080 A295083 A180877

Adjacent sequences: A280265 A280266 A280267 * A280269 A280270 A280271

Keyword

nonn,more

Author

Altug Alkan, Dec 31 2016

Extensions

a(10)-a(14) from Amiram Eldar, May 19 2024

Status

approved