A084322 Fixed points if prime-factor-concatenation function (A084318) is iterated at primorial number initial values.

2, 23, 547, 2357, 4359293547691, 325798243129564339, 3947306373286437248759663633906484193454376823

Offset

1,1

Links

Table of n, a(n) for n=1..7.

Formula

a(n)=A084318[A002110(n)]

Example

n=4: primorial[4]=2310; a(4)=4359293547691=A084318[2310]; the list of iterations:
{2310, 235711, 7151223, 34495309, 41841349, 1116722777, 1958774883, 313113444469, 744730492067, 4359293547691};
at each step the ordered prime factors of previous term are concatenated.

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]] lf[x_] := Length[FactorInteger[x]] nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] coc[x_] := Fold[nd, 0, Flatten[IntegerDigits[ba[x]], 1]] Table[FixedPoint[coc, q[w]], {w, 1, 7}]

Crossrefs

Cf. A001405, A084317, A084318.

Sequence in context: A053161 A090731 A090314 * A073062 A015098 A269021

Adjacent sequences: A084319 A084320 A084321 * A084323 A084324 A084325

Keyword

base,nonn

Author

Labos Elemer, Jun 20 2003

Status

approved