A278311 Numbers n such that n-1 and n+1 have the same number of prime factors as n (with multiplicity).

34, 86, 94, 122, 142, 171, 202, 214, 218, 245, 285, 302, 394, 429, 435, 446, 507, 603, 604, 605, 634, 638, 698, 842, 922, 963, 1042, 1075, 1084, 1085, 1131, 1138, 1245, 1262, 1275, 1310, 1346, 1402, 1413, 1431, 1435, 1449, 1491, 1533, 1557, 1587, 1605, 1635, 1642, 1676, 1762, 1772, 1838, 1886, 1894, 1925, 1942

Offset

1,1

Links

Ely Golden, Table of n, a(n) for n = 1..10000

Example

a(1) = 34, as 33, 34, and 35 all have 2 prime factors.
a(2) = 86, as 85, 86, and 87 all have 2 prime factors.

Prog

(Java) public class A278311{
public static void main(String[] args)throws Exception{
    long dim0=numberOfPrimeFactors(2); //note that this method must be manually implemented by the user
    long dim1=numberOfPrimeFactors(3);
    long dim2;
    long counter=4;
    long index=1;
    while(index<=10000){
      dim2=numberOfPrimeFactors(counter);
      if(dim2==dim1&&dim1==dim0){System.out.println(index+" "+(counter-1)); index++; }
      dim0=dim1;
      dim1=dim2;
      counter++;
    }
  }
}
(SageMath)
def bigomega(x):
    s=0;
    f=list(factor(x));
    for c in range(len(f)):
        s+=f[c][1]
    return s;
dim0=bigomega(2);
dim1=bigomega(3);
counter=4
index=1
while(index<=10000):
    dim2=bigomega(counter);
    if(dim2==dim1&dim1==dim0):
        print(str(index)+" "+str(counter-1))
        index+=1;
    dim0=dim1;
    dim1=dim2;
    counter+=1;
(PARI) isok(n) = (bigomega(n-1) == bigomega(n)) && (bigomega(n) == bigomega(n+1)); \\ Michel Marcus, Nov 17 2016

Crossrefs

Intersection of A045920 and A278291.

a(n) = A045939(n) + 1.

Sequence in context: A092223 A046764 A260276 * A213025 A365200 A086005

Adjacent sequences: A278308 A278309 A278310 * A278312 A278313 A278314

Keyword

nonn

Author

Ely Golden, Nov 17 2016

Status

approved