A225914 Position of the first occurrence of n in sequence A196942.

3, 7, 23, 71, 311, 461, 799, 1271, 719, 941, 967, 1151, 1783, 1847, 2659, 1621, 3067, 1663, 3583, 2467, 2851, 2551, 4051, 5741, 6239, 6373, 6271, 5927, 8627, 6841, 5603, 4201, 5581, 9901, 6037, 8423, 7487, 7123, 5867, 5791, 6011, 8539, 13119, 6367, 13327, 11863

Offset: 1

Author

Lei Zhou, May 20 2013

Keywords

• nonn

Comments

a(n) is also the smallest positive integer such that the prime number order of p3 has to be n or larger when a(n) is written as a(n) = p1^m1 * p2^m2 * p3^m3 + p1^n1 * p2^n2 * p3^n3, where p1 < p2 < p3 are prime numbers and m1,m2,m3 and n1,n2,n3 are integers greater than or equal to zero.

Examples

			1 appears first at position 3 in A196942, so a(1)=3;
3 appears first at position 23 in A196942, so a(3)=23.
		

Links

• Lei Zhou, Table of n, a(n) for n = 1..186

Crossrefs

Cf. A000040, A196491, A196492.

Programs

Mathematica

max = 46; res = Table[0, {i, 1, max}]; i = 1; ct = 0; While[ct < max, i++; ref = i; Do[k = i - j; fj = Transpose[FactorInteger[j]][[1]]; fk = Transpose[FactorInteger[k]][[1]]; fpls = Union[fj, fk]; lf = Length[fpls]; If[lf <= 3, cd = fpls[[lf]]; If[cd < ref, ref = cd]], {j,Ceiling[i/2], i}]; tag = PrimePi[ref]; If[tag <= max, If[res[[tag]] == 0, res[[tag]] = i; ct++]]]; res