A060847 - OEIS

A060847

Difference between a nontrivial prime power (A246547) and the previous prime.

1, 1, 2, 3, 2, 4, 1, 2, 3, 2, 8, 12, 1, 2, 2, 5, 6, 6, 2, 3, 6, 6, 2, 2, 8, 3, 4, 2, 12, 2, 9, 8, 18, 2, 2, 6, 4, 12, 2, 3, 6, 4, 2, 6, 12, 8, 2, 6, 2, 1, 6, 8, 2, 2, 14, 4, 6, 2, 6, 2, 3, 20, 2, 12, 2, 2, 8, 14, 10, 18, 8, 6, 2, 2, 2, 12, 12, 19, 2, 6, 6, 20, 2, 2, 2, 8, 8, 2, 2, 8, 20, 12, 15, 2, 4

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OFFSET

1,3

COMMENTS

a(n)=1 only for some powers of 2.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A246547(n)-prevprime(A246547(n)) = A246547(n)-A049711(A246547(n)).

EXAMPLE

78125=5^7 follows 78121, the difference is 4.

MAPLE

N:= 10^5: # to consider prime powers <= N

P:= select(isprime, [2, seq(i, i=3..floor(sqrt(N)), 2)]):

PP:= sort([seq(seq(p^k, k=2..ilog[p](N)), p=P)]):

map(t -> t - prevprime(t), PP); # Robert Israel, Nov 13 2024

PROG

(Python)

from sympy import primepi, integer_nthroot, prevprime

def A060847(n):

def f(x): return int(n+x-sum(primepi(integer_nthroot(x, k)[0]) for k in range(2, x.bit_length())))

def bisection(f, kmin=0, kmax=1):

while f(kmax) > kmax: kmax <<= 1

while kmax-kmin > 1:

kmid = kmax+kmin>>1

if f(kmid) <= kmid:

kmax = kmid

else:

kmin = kmid

return kmax

return (a:=bisection(f, n, n))-prevprime(a) # Chai Wah Wu, Sep 13 2024

CROSSREFS

Cf. A025475, A000961, A001597, A001694, A007917, A007918, A013632, A013633, A049711, A246547.

Sequence in context: A208083 A181515 A183045 * A079528 A143422 A071438

Adjacent sequences: A060844 A060845 A060846 * A060848 A060849 A060850

KEYWORD

nonn

AUTHOR

Labos Elemer, May 03 2001

STATUS

approved