

A256705


Numbers n such that if we define f(n,m) by the recursion f(n,1)=n, f(n,k+1)= A007672(n,k), the subsequence f(n,k), with n constant, is eventually periodic with period two.


0



9, 16, 25, 45, 49, 63, 75, 80, 81, 99, 112, 117, 121, 125, 128, 147, 153, 169, 171, 175, 176, 207, 208, 225, 243, 245, 250, 256, 261, 275, 279, 289, 304, 315, 325, 333, 343, 361, 363, 368, 369, 375, 387, 405, 423, 425, 441, 464, 475, 477, 486, 495, 496, 500, 507, 512, 525, 529, 531, 539, 549, 560
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OFFSET

1,1


COMMENTS

If n is in the sequence, there is an index k such that, for m>=k, S(f(n,m))=S(f(n,m+1)), where S(n) is Kempner function A002034(n).
If n is not in the sequence, there is an index k such that S(f(n,m))>S(f(n,m+1)) for m<k, and f(n,m)=1 for m>=k.


LINKS

Table of n, a(n) for n=1..62.


EXAMPLE

16 is in the sequence because f(16,1) = 16, f(16,2) = A007672(16) = 45, f(16,3) = A007672(45) = 16, f(16,4) = A007672(16) = 45, ..., a sequence with period 2.
15 is not in the sequence, then f(15,1) = 15, f(15,2) = A007672(15) = 8, f(15,3) = A007672(8) = 3, f(15,4) = A007672(3) = 2, f(15,5) = A007672(2) = 1, f(15,6) = A007672(1) = 1, ..., a sequence with period 1.


PROG

(PARI) b(n)=my(m=1, x=n, as=1, p); while(x>1, m++; p=gcd(x, m); x/=p; as*=m/p); as /* A007672(n) */
for(i=1, 10^3, m=i; v=1; while(m>1&&v, n=b(m); if(m==b(n), v=0; print1(i, ", ")); m=n))


CROSSREFS

Cf. A000142, A002034, A007672.
Sequence in context: A026062 A108945 A177430 * A092941 A075393 A161183
Adjacent sequences: A256702 A256703 A256704 * A256706 A256707 A256708


KEYWORD

nonn


AUTHOR

Antonio Roldán, Apr 08 2015


STATUS

approved



