

A155850


a(n) = smallest k > 1 such that k1 and k+1 together have n prime divisors.


1



2, 4, 3, 5, 7, 15, 17, 31, 65, 129, 127, 449, 511, 2561, 1025, 7937, 12799, 20481, 8191, 28673, 65537, 131071, 458751, 360449, 966655, 524287, 4194303, 2097151, 29360129, 34865153, 67108865, 134217729, 33554431, 608174081, 268435457, 536870911, 4831838207
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Prime divisors are counted with multiplicity.
Similar to A155800, where k is restricted to primes.
Terms of the form 2^m1 or 2^m+1 seem to occur frequently.


LINKS



EXAMPLE

Adjacent to 2 are the numbers 1 and 3 which together have one prime divisor, hence a(1) = 2. Adjacent to 3 are 2 and 4; together they have three prime divisors, hence a(3) = 3. Adjacent to 4 are the primes 3 and 5, each having one prime divisor; hence a(2) = 4.
For k = 129, k1 = 128 = 2*2*2*2*2*2*2 and k+1 = 130 = 2*5*13 together have ten prime divisors. For all numbers k < 129 the adjacent numbers k1 and k+1 together have fewer or more than ten (for 127 there are eleven) prime divisors, hence a(10) = 129.


PROG

(PARI) {for(n=2, 150000000, s=bigomega(n1)+bigomega(n+1); if(v[s]==0, v[s]=n)); v}


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



