A077655 Number of consecutive successors of n having the same number of prime factors as n (counted with multiplicity).

0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset

1,33

Comments

If a(n) > 0 then a(n+1) = a(n)-1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Example

33=3*11 has only two successors also with two factors: 34=2*17 and 35=5*7 (whereas 33+3=36=2*2*3*3), therefore a(33)=2.

Mathematica

snpf[n_]:=Module[{f=PrimeOmega[n], k=0}, While[f==PrimeOmega[n+k], k++]; k]; Array[snpf, 110]-1 (* Harvey P. Dale, Aug 01 2021 *)

Prog

(PARI) A077655(n) = { my(k=n+1, w=bigomega(n)); while(bigomega(k)==w, k++); (k-n)-1; }; \\ Antti Karttunen, Jan 22 2020

Crossrefs

Cf. A001222, A077656, A045920, A045939, A045940, A045941, A045942, A077657.

Sequence in context: A343870 A339070 A352553 * A117886 A145723 A085977

Adjacent sequences: A077652 A077653 A077654 * A077656 A077657 A077658

Keyword

nonn

Author

Reinhard Zumkeller, Nov 13 2002

Status

approved