A053063 Pendulum numbers: alternately append n to beginning or end of previous term.

1, 21, 213, 4213, 42135, 642135, 6421357, 86421357, 864213579, 10864213579, 1086421357911, 121086421357911, 12108642135791113, 1412108642135791113, 141210864213579111315, 16141210864213579111315, 1614121086421357911131517, 181614121086421357911131517, 18161412108642135791113151719

Offset

1,2

Comments

Comments from N. J. A. Sloane, Dec 07 2019: (Start)

Eric Angelini and Kay Rosen suggest these could be called Pnuumlde numbers.

Eric Angelini asks if any term is a prime.

James R. Buddenhagen finds that the first prime is a(121), a 255-digit prime according to Maple.

Hans Havermann finds that there is one more prime in the first 10000 terms, a(1399), which is a 4489-digit prime.

(End)

The third prime in the sequence is a(40714) with 192464 decimal digits. The terms at even indices are duplicated by the even-indexed terms of A281254, which is why this term is a prime for both sequences. - Hans Havermann, Jan 16 2020

Links

Harvey P. Dale, Table of n, a(n) for n = 1..369

Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000.

Mathematica

nxt[{n_, a_}]:={n+1, If[OddQ[n], (n+1)*10^IntegerLength[a]+a, a*10^IntegerLength[ n+1]+ n+1]}; NestList[nxt, {1, 1}, 30][[All, 2]] (* Harvey P. Dale, Jul 20 2022 *)

Prog

(PARI) lista(nn) = {print1(val=1, ", "); b = 0; for (n=2, nn, if (b, val = concat(Str(val), Str(n)), val = concat(Str(n), Str(val))); print1(val, ", "); b = 1 - b; ); } \\ Michel Marcus, Aug 11 2017

Crossrefs

See A281254 for another version.

Sequence in context: A133355 A041846 A120786 * A060933 A075282 A228681

Adjacent sequences: A053060 A053061 A053062 * A053064 A053065 A053066

Keyword

easy,nonn,base

Author

Felice Russo, Feb 25 2000

Extensions

More terms from Michel Marcus, Aug 11 2017

Status

approved