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A137328 a(n) = prime(n) - primorial(k), where k is the greatest number for which primorial(k) <= prime(n). 1
0, 1, 3, 1, 5, 7, 11, 13, 17, 23, 1, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 49, 53, 59, 67, 71, 73, 77, 79, 83, 97, 101, 107, 109, 119, 121, 127, 133, 137, 143, 149, 151, 161, 163, 167, 169, 1, 13, 17, 19, 23, 29, 31, 41, 47, 53, 59, 61, 67, 71, 73, 83, 97, 101, 103, 107, 121 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Conjecture: Each prime number appears in this sequence at least once.
Is there any general asymptotic formula for the appearance of prime(n) in this sequence?
LINKS
EXAMPLE
a(6) = prime(6) - primorial(2) = 13 - 6 = 7.
PROG
(PARI) a(n) = {my(p=prime(n), q=1, P=1); until (P > p, q = nextprime(q+1); P *= q; ); p - P/q; } \\ Michel Marcus, Mar 14 2022
(Python)
from sympy import nextprime
from itertools import islice
def agen(): # generator of terms
pn, primk, pk, pkplus = 2, 2, 2, 3
while True:
while primk * pkplus <= pn:
primk, pk, pkplus = primk*pkplus, pkplus, nextprime(pkplus)
yield pn - primk
pn = nextprime(pn)
print(list(islice(agen(), 67))) # Michael S. Branicky, Mar 14 2022
CROSSREFS
Sequence in context: A354576 A049764 A136437 * A140991 A302191 A261712
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Apr 07 2008
STATUS
approved

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Last modified July 23 06:59 EDT 2024. Contains 374544 sequences. (Running on oeis4.)