A115186 Smallest number m such that m and m+1 have exactly n prime factors (counted with multiplicity).

2, 9, 27, 135, 944, 5264, 29888, 50624, 203391, 3290624, 6082047, 32535999, 326481920, 3274208000, 6929459199, 72523096064, 37694578688, 471672487935, 11557226700800, 54386217385983, 50624737509375, 275892612890624, 4870020829413375, 68091093855502335, 2280241934368767

Offset

1,1

Comments

A001222(a(n)) = A001222(a(n)+1) = n: subsequence of A045920.

a(16) > 4*10^10. - Martin Fuller, Jan 17 2006

a(n) <= A093548(n) <= A052215(n). - Zak Seidov, Jan 16 2015

Apparently, 4*a(n)+2 is the least number k such that k-2 and k+2 have exactly n+2 prime factors, counted with multiplicity. - Hugo Pfoertner, Apr 02 2024

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 135, p. 46, Ellipses, Paris 2008.

Links

Table of n, a(n) for n=1..25.

Example

a(10) = 3290624 = 6427 * 2^9, 3290624+1 = 13 * 5^5 * 3^4:
A001222(3290624) = A001222(3290625) = 10.

Crossrefs

Cf. A001222, A045920, A052215, A093548.

Equivalent sequences for longer runs: A113752 (3), A356893 (4).

Sequence in context: A123904 A327612 A019065 * A243560 A090900 A357721

Adjacent sequences: A115183 A115184 A115185 * A115187 A115188 A115189

Keyword

nonn

Author

Reinhard Zumkeller, Jan 16 2006

Extensions

a(13)-a(15) from Martin Fuller, Jan 17 2006

a(16)-a(17) from Donovan Johnson, Apr 08 2008

a(18)-a(22) from Donovan Johnson, Jan 21 2009

a(23)-a(25) from Donovan Johnson, May 25 2013

Status

approved