A282770 a(1)=1. For n>1, start with n, concatenate the indices of its prime factors, and repeat until either (i) a prime p is reached, when we set a(n)=p; or (ii) the process enters a loop of length m, when we set a(n) = -m; or (iii) the trajectory diverges to infinity, when we set a(n) = 0.

1, 2, 3, 11, 5, 1733, 7, 12637, 23, 13, 11, 1733, 13, -1, 23, 1103, 17, 1117, 19, 113, 1277, 23, 23, 1277, -2, 1103, 1801, 222312455509, 29, 349, 31, 1439, -2, 17, 17, 281, 37, 1117, 1103, 121327, 41, 1103, 43, 1103, 223, 19, 47, 11369, 1103, 11369, 1801, 11147108327

Offset

1,2

Comments

A loop of length 3 is reached with the initial number 714: 714=2*3*7*17 = p_1*p_2*p_4*p_7 -> 1247=29*43 = p_10*p_14 -> 1014=2*3*13*13 -> 1266=2*3*211 -> 1247. The loop is 1247 -> 1014 -> 1266.

Links

Table of n, a(n) for n=1..52.

Example

10=2*5 -> 2=prime(1), 5=prime(3) -> 13, prime, so a(10)=13.
25=5*5 -> 5=prime(3) -> 33 = 3*11 -> 3=prime(2), 11=prime(5) -> 25 (the initial number) -> loop: 25-33-25-33-... -> loop of length 2, so a(25)=-2.

Mathematica

f[n_] := FromDigits@ Flatten@ IntegerDigits@ Table[PrimePi@ e[[1]] + 0 Range@ e[[2]], {e, FactorInteger@n}]; a[1]=1; a[n_]:= Block[{z}, z = NestWhileList[f, n, (! PrimeQ@ Last@ List@ ## && Unequal@ ##) &, All]; If[ PrimeQ@ Last@ z, Last@ z, First[ Subtract @@ Position[z, Last@ z]]]]; Array[a, 39] (* Giovanni Resta, Sep 01 2019 *)

Crossrefs

Cf. A037274 (home primes).

Sequence in context: A269253 A084047 A354585 * A145077 A127376 A086146

Adjacent sequences: A282767 A282768 A282769 * A282771 A282772 A282773

Keyword

sign,base

Author

Peter Weiss, Mar 01 2017

Extensions

Definition revised by N. J. A. Sloane, Mar 07 2017

More terms from Giovanni Resta, Sep 01 2019

Status

approved