A063383 a(1) = 6, a(n) = concatenation of two closest divisors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).

6, 23, 123, 341, 1131, 2939, 12939, 57227, 89643, 329881, 1073083, 1197553, 7171079, 17171079, 57301247, 208327509, 1171780577, 1219684137, 1478297171, 2587571433, 2795835979, 8663322733, 13666409441, 113666409441, 1030771102733, 2114885171103, 6993025586797

Offset: 1

Author

Robert G. Wilson v, Aug 08 2001

Keywords

• base
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A003681, A062094 and A062095.

Programs

Mathematica

f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[[ l/2 ] ] ] <> ToString[ d[[ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[[ l/2 + .5 ] ] ] <> ToString[ d[[ l/2 + .5 ] ] ] ] ] ); NestList[ f, 6, 25 ]
tcf[n_]:=Module[{d=Divisors[n],len},len=Length[d]/2;FromDigits[Flatten[ IntegerDigits/@Take[d,{len,len+1}]]]]; ctc[n_]:=If[PrimeQ[ n], 10^IntegerLength[ n]+n,tcf[n]]; NestList[ctc,6,30] (* Harvey P. Dale, May 19 2019 *)

Python

from sympy import divisors, isprime
def aupton(terms):
    alst = [6]
    for n in range(2, terms+1):
        if isprime(alst[-1]): alst.append(int('1' + str(alst[-1])))
        else:
            divs = divisors(alst[-1])
            d1 = divs[(len(divs)-1)//2]
            d2 = alst[-1]//d1
            alst.append(int(str(d1) + str(d2)))
    return alst
print(aupton(27)) # Michael S. Branicky, Jun 23 2021

Extensions

Definition clarified by Harvey P. Dale, May 19 2019