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A224748
Given n-th prime p, a(n) = number of primes of the form p + q - 1 where q is any prime < p.
14
0, 0, 1, 1, 2, 3, 3, 3, 2, 3, 6, 6, 5, 8, 4, 4, 4, 11, 11, 8, 9, 11, 4, 5, 13, 9, 11, 7, 13, 5, 17, 10, 9, 15, 7, 19, 17, 18, 10, 8, 8, 25, 12, 17, 12, 18, 29, 23, 12, 21, 12, 15, 28, 18, 11, 11, 12, 32, 25, 19, 22, 14, 29, 17, 27, 14, 40, 36, 18, 29, 16, 13
OFFSET
1,5
COMMENTS
Conjecture: a(n)>0 for all n>2. - Dmitry Kamenetsky, Feb 09 2017
LINKS
MAPLE
a:= n-> add(`if`(isprime(ithprime(n)+ithprime(i)-1), 1, 0), i=1..n-1):
seq(a(n), n=1..100); # Alois P. Heinz, Apr 18 2013
MATHEMATICA
Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p + Prime[i] - 1], c = c + 1]; i++]; c, {n, 72}]
Table[Count[Prime[n]+Prime[Range[n-1]]-1, _?PrimeQ], {n, 80}] (* Harvey P. Dale, Nov 04 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jayanta Basu, Apr 17 2013
STATUS
approved