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

1,1

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.

Links

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

Example

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

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

Crossrefs

Cf. A000040, A196491, A196492.

Sequence in context: A045723 A140456 A066768 * A062241 A000229 A133435

Adjacent sequences: A225911 A225912 A225913 * A225915 A225916 A225917

Keyword

nonn

Author

Lei Zhou, May 20 2013

Status

approved