OFFSET
1,1
COMMENTS
Each prime is just listed once, though it may arise in more than one way.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 73 is a term because it is prime and Sum_{i=0..2} binomial(2,i)*prime(11+i) = 31+2*37+41 = 2*73.
a(10) = 257 arises in two ways:
2*257 = Sum_{i=0..3} binomial(3,i)*prime(17+i) = 59+3*61+3*67+71
and Sum_{i=0..4} binomial(4,i)*prime(9+i) = 23+4*29+6*31+4*37+41.
MAPLE
N:= 10^4: # for terms <= N
S:= {}:
for m from 2 do
for k from 2 do
v:= add(binomial(m, i)*ithprime(i+k), i=0..m)/2;
if v > N then break fi;
if isprime(v) then
S:= S union {v}; count:= count+1;
fi;
od;
if k = 2 then break fi
od:
sort(convert(S, list));
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Feb 28 2021
STATUS
approved