A134070 Primes in A130774.

13, 13471118294776123, 134711182947761231993225218431364220735715778934915127244763960364079103682167761271443439204710647114985118604983010349

Offset

1,1

Comments

A130774 = {1, 13, 134, 1347, 134711, 13471118, 1347111829, 134711182947, 13471118294776, 13471118294776123, ...} = Concatenate Lucas numbers. Indices of prime terms in A130774 are {2, 10, 31, ...}.

a(4) > A130774(500) = 1.347...*10^26425, if it exists. - Amiram Eldar, Jul 17 2025

Links

Table of n, a(n) for n=1..3.

Eric Weisstein's World of Mathematics, Lucas Number.

Eric Weisstein's World of Mathematics, Smarandache Sequences.

Example

a(1) = A130774(2) = 13.
a(2) = A130774(10) = 13471118294776123.
a(3) = A130774(31) = 13471118294776123199322521843136422073571577893491512724476396036407910368216776127144343920471064711498511860498301034.

Mathematica

Select[Module[{nn=40, ll}, ll=LucasL[Range[nn]]; Table[FromDigits[Flatten[IntegerDigits/@Take[ll, n]]], {n, nn}]], PrimeQ] (* Harvey P. Dale, May 07 2023 *)

Crossrefs

Cf. A000204 (Lucas numbers).

Cf. A130774 (concatenation of Lucas numbers).

Cf. A019523 (concatenation of Fibonacci numbers).

Cf. A038399 (concatenation of first n nonzero Fibonacci numbers in reverse order).

Cf. A134072 (concatenation of A000204 Lucas numbers (beginning at 1) in reverse order).

Cf. A134069 (primes in A038399).

Cf. A134071 (primes in A134072).

Sequence in context: A048847 A093671 A257137 * A257308 A257369 A322517

Adjacent sequences: A134067 A134068 A134069 * A134071 A134072 A134073

Keyword

nonn,base,bref,hard

Author

Alexander Adamchuk, Oct 06 2007

Extensions

Edited by Charles R Greathouse IV, Apr 24 2010

Status

approved