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 A083021 a(n) = the number of distinct primes of the form p(n)#/p(i) + p(i). 1
 1, 1, 3, 4, 3, 4, 3, 2, 2, 5, 2, 4, 2, 2, 6, 2, 3, 4, 4, 3, 5, 1, 3, 3, 3, 2, 3, 3, 6, 2, 1, 0, 0, 1, 2, 6, 2, 3, 1, 7, 3, 1, 1, 2, 0, 1, 4, 4, 2, 4, 4, 0, 3, 3, 4, 1, 2, 4, 2, 2, 1, 2, 2, 2, 1, 3, 2, 1, 4, 3, 2, 3, 2, 3, 3, 4, 5, 2, 2, 5, 4, 2, 2, 1, 2, 2, 1, 5, 0, 2, 1, 2, 4, 2, 4, 4, 1, 5, 1, 1, 1, 3, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Some of the larger entries may only correspond to probable primes. LINKS EXAMPLE p(n) is the n-th prime; # denotes primorial (A002110). a(2)=1 because 3#/2+2 and 3#/3+3 are the same prime (5). a(4)=4 because 7#/2+2=107, 7#/3+3=73, 7#/5+5=47, 7#/7+7=37 are four primes. PROG (PARI) p_n_primorial(n) = prod(i=1, n, prime(i)) { for(n=3, 200, p=p_n_primorial(n); c=0; for(i=1, n, q=p/prime(i)+prime(i); if(isprime(q), c++)); print1(c, ", ")) } CROSSREFS Cf. A002110. Sequence in context: A270827 A293072 A120447 * A102745 A108026 A010702 Adjacent sequences:  A083018 A083019 A083020 * A083022 A083023 A083024 KEYWORD nonn AUTHOR Rick L. Shepherd, May 31 2003 EXTENSIONS Edited by Don Reble, Nov 16 2005 STATUS approved

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Last modified September 20 22:45 EDT 2021. Contains 347596 sequences. (Running on oeis4.)