A085651 Index of the first of two successive 2's in A005361.

44, 49, 75, 98, 116, 147, 171, 244, 260, 275, 315, 332, 363, 387, 475, 476, 507, 524, 531, 548, 549, 603, 604, 636, 692, 724, 725, 747, 764, 774, 819, 844, 845, 846, 867, 908, 924, 931, 963, 1035, 1075, 1083, 1179, 1196, 1251, 1274, 1275, 1324, 1340, 1395

Offset: 1

Author

Amarnath Murthy, Jason Earls, Jul 11 2003

Keywords

• easy
• nonn

Comments

Numbers such that bigomega(n) - omega(n) = 1 and bigomega(n+1) - omega(n+1) = 1, where bigomega(n) is the number of primes dividing n (counted with repetition) and omega(n) is the number of distinct primes dividing n. - Michel Lagneau, Dec 17 2011

Elements of A060687 whose successor is also in A060687. - Emmanuel Vantieghem, Mar 05 2017

This sequence has 3548 terms up to 10^5, 35340 up to 10^6, 353147 up to 10^7, and 3531738 up to 10^8, suggesting a natural density around 0.0353.... - Charles R Greathouse IV, Mar 06 2017

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Indranil Ghosh)
• Indranil Ghosh, Python program to generate the sequence.

Crossrefs

Cf. A005361, A060687.

Programs

Mathematica

Select[Range[1400],PrimeOmega[#]-PrimeNu[#] == 1 && PrimeOmega[#+1] - PrimeNu[#+1] == 1 &] (* Indranil Ghosh, Mar 05 2017 *)
SequencePosition[Table[PrimeOmega[n]-PrimeNu[n],{n,1500}],{1,1}][[;;,1]] (* Harvey P. Dale, Jul 17 2024 *)

PARI

isok(n) = (bigomega(n)-omega(n) == 1) && (bigomega(n+1)-omega(n+1) == 1); \\ Michel Marcus, Mar 05 2017

PARI

is(n)=factorback(factor(n)[,2])==2 && factorback(factor(n+1)[,2])==2 \\ Charles R Greathouse IV, Mar 06 2017