A240590 Number of primes between successive powerful numbers (A001694).

2, 2, 0, 2, 3, 0, 2, 0, 4, 3, 2, 2, 3, 3, 2, 0, 1, 3, 5, 5, 2, 1, 1, 5, 1, 7, 0, 5, 2, 4, 5, 1, 5, 2, 7, 3, 2, 2, 6, 9, 4, 4, 0, 7, 8, 2, 7, 4, 4, 8, 1, 1, 4, 4, 9, 7, 2, 1, 9, 10, 6, 1, 0, 2, 0, 9, 12, 7, 4, 12, 6, 5, 4, 5, 12, 0, 8, 3, 3, 10, 8, 0, 2, 13, 2, 13, 10, 10, 1, 15, 0, 7, 9, 9, 3, 13, 7, 4, 0, 7, 5, 4, 13, 2

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(9) = 4 because A001694(9) = 36, A001694(10) = 49, and there are 4 primes between them: 37, 41, 43 and 47.

Prog

(PARI)
ispowerful(n)={local(h); if(n==1, h=1, h=(vecmin(factor(n)[, 2])>1)); return(h)}
proxpowerful(n)={local(k); k=n+1; while(!ispowerful(k), k+=1); return(k)}
{for(i=1, 5000, if(ispowerful(i), m=proxpowerful(i); p=primepi(m)-primepi(i); print1(p, ", ")))}

Crossrefs

Cf. A001694, A240591.

Sequence in context: A141661 A278521 A195910 * A080769 A328903 A143539

Adjacent sequences: A240587 A240588 A240589 * A240591 A240592 A240593

Keyword

nonn

Author

Antonio Roldán, Apr 08 2014

Status

approved