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A069922 Number of primes p such that n^n <= p <= n^n + n^2. 0
1, 2, 2, 4, 1, 5, 4, 1, 2, 5, 1, 4, 4, 9, 7, 6, 2, 4, 7, 9, 7, 3, 7, 10, 10, 6, 12, 6, 10, 7, 8, 10, 7, 9, 13, 13, 7, 10, 11, 11, 9, 13, 11, 10, 15, 10, 11, 10, 19, 14, 16, 11, 16, 21, 20, 12, 9, 15, 21, 12, 10, 16, 15, 22, 19, 17, 18, 12, 19, 20, 13, 17, 13, 13, 17, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Question: for any n>0, is there at least one prime p such that n^n <= p <= n^n + n^2? In this case, that would be stronger than the Schinzel conjecture: "for m > 1 there's at least one prime p such that m <= p <= m + log(m)^2" since n^2 < log(n^n)^2 = n^2*log(n)^2.

LINKS

Table of n, a(n) for n=1..76.

PROG

(PARI) for(n=1, 65, print1(sum(i=n^n, n^n+n^2, isprime(i)), ", "))

CROSSREFS

Cf. A000040, A216266, A217317.

Sequence in context: A066202 A027420 A116588 * A072211 A328925 A299020

Adjacent sequences:  A069919 A069920 A069921 * A069923 A069924 A069925

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 05 2002

EXTENSIONS

a(66)-a(76) from Alex Ratushnyak, Apr 20 2014

STATUS

approved

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Last modified May 7 19:23 EDT 2021. Contains 343652 sequences. (Running on oeis4.)