

A196558


a(n) is the index of the first occurrence of n in A195061.


0




OFFSET

1,1


COMMENTS

In sequence A195061, element 2 through 25 are 1, which means it is possible to find a sum of p=b+c, p is the nth prime number, the prime factors of b and c traverse all primes smaller than square root p(n). From element 36, the above case does no longer stand for most of primes. However, if you pick two eligible sum p=b1+c1=b2+c2, it becomes possible that the union set of prime factors of b1, c1, b2, and c2 traverse all primes smaller than square root p(n). This stands until p(107)=587. For p(108)=593, no group of two b and cs can have the union set of their prime factors to traverse all primes smaller than square root p(n). Three groups of b and cs will be needed to do so. And starting from p(284)=1861, four groups are needed for some of the numbers.
The listed Mathematica program failed in finding a(5) since it exceeded the integer range as index.


LINKS

Table of n, a(n) for n=1..4.


EXAMPLE

A195061[2]=1 => a(1)=2;
A195061[3]=A195061[4]=...=A195061[35]=1; A195061[36]=2 => a(2)=36;
A195061[1..107]<=2; A195061[108]=3 => a(3)=108;
A195061[1..283]<=3; A195061[284]=4 => a(4)=284;


MATHEMATICA

(* Taking the function Checks[n_] in the Mathematica program for A195061, the following program gives the first four terms: *) k = 0; i = 1; a = 0; Array[ff, 4]; Do[ff[j] = 0, {j, 1, 4}]; While[(k < 4) && (a < 4), i++; a = Checks[i]; If[(a <= 4) && (ff[a] == 0), ff[a] = i; k++]]; Table[ff[m], {m, 4}]


CROSSREFS

Cf. A196526, A195061.
Sequence in context: A278930 A258356 A145450 * A187509 A134785 A143745
Adjacent sequences: A196555 A196556 A196557 * A196559 A196560 A196561


KEYWORD

nonn,hard,bref


AUTHOR

Lei Zhou, Oct 03 2011


STATUS

approved



