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

Author

Antonio Roldán, Apr 08 2015

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A000142, A002034, A007672.

Programs

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))