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

Author

Felice Russo, Feb 25 2000

Keywords

• easy
• nonn
• base

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.

Crossrefs

See A281254 for another version.

Programs

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 *)

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

Extensions

More terms from Michel Marcus, Aug 11 2017