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.

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

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 A336449

Adjacent sequences: A256702 A256703 A256704 * A256706 A256707 A256708

Keyword

nonn

Author

Antonio Roldán, Apr 08 2015

Status

approved