A294280 a(n) = least positive k such that omega(n+k) > max(omega(n), omega(k)), where omega(m) = A001221(m), the number of distinct primes dividing m.

1, 4, 3, 2, 1, 24, 3, 2, 1, 20, 1, 18, 1, 16, 15, 2, 1, 12, 1, 10, 9, 8, 1, 6, 1, 4, 1, 2, 1, 180, 2, 1, 9, 8, 7, 6, 1, 4, 3, 2, 1, 168, 1, 16, 15, 14, 1, 12, 1, 10, 9, 8, 1, 6, 5, 4, 3, 2, 1, 150, 1, 4, 3, 1, 1, 144, 1, 2, 1, 140, 1, 6, 1, 4, 3, 2, 1, 132, 1

Offset

1,2

Comments

For any n > 0, a(n) <= n * (A053669(n) - 1).

Apparently, a(n) = n * (A053669(n) - 1) iff n belongs to A077011.

a(n) = 1 iff omega(n) < omega(n+1).

a(p) = 1 for any prime power p not in A006549.

The scatterplot of the sequence shows segments of slope -1, corresponding to frequent values of n+a(n); these segments correspond to the strands in the plot of the ordinal transform of n+a(n) (see plots in Links section).

Links

Table of n, a(n) for n=1..79.

Rémy Sigrist, Logarithmic scatterplot of the first 10000 terms

Rémy Sigrist, Pin plot of the first 10000 terms

Rémy Sigrist, Ordinal transform of the first 10000 terms of n+a(n)

Example

For n=2:
- omega(2+1) = 1 = omega(2),
- omega(2+2) = 1 = omega(2),
- omega(2+3) = 1 = omega(2),
- omega(2+4) = 2 > max(omega(2), omega(4)) = 1,
- hence, a(2) = 4.

Prog

(PARI) a(n) = my (on=omega(n)); for (k=1, oo, if (omega(n+k) > max(on, omega(k)), return (k)))

Crossrefs

Cf. A001221, A006549, A053669, A077011, A294277.

Sequence in context: A349727 A129154 A055115 * A108438 A347738 A082504

Adjacent sequences: A294277 A294278 A294279 * A294281 A294282 A294283

Keyword

nonn

Author

Rémy Sigrist, Oct 26 2017

Status

approved