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A342093
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Primes that can be represented as (1/2)*Sum_{i=0..m} binomial(m,i)*prime(i+k) for some k and m >= 2.
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1
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47, 61, 73, 103, 137, 157, 167, 179, 223, 257, 263, 337, 347, 383, 467, 563, 613, 719, 733, 757, 769, 877, 887, 1021, 1097, 1223, 1297, 1327, 1367, 1453, 1481, 1571, 1613, 1621, 1759, 1811, 1987, 1997, 2003, 2027, 2039, 2129, 2251, 2473, 2477, 2539, 2593, 2633, 2767, 2879, 3001, 3037, 3083, 3119
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OFFSET
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1,1
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COMMENTS
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Each prime is just listed once, though it may arise in more than one way.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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