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

1,1

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.

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 *)

Prog

(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

Crossrefs

Cf. A005361, A060687.

Sequence in context: A088066 A116355 A071318 * A066124 A270298 A231402

Adjacent sequences: A085648 A085649 A085650 * A085652 A085653 A085654

Keyword

easy,nonn

Author

Amarnath Murthy, Jason Earls, Jul 11 2003

Status

approved