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 A342093 Primes that can be represented as (1/2)*Sum_{i=0..m} binomial(m,i)*prime(i+k) for some k and m >= 2. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 Contains A338273. Sequence in context: A139909 A368077 A243430 * A126980 A354442 A354461 Adjacent sequences: A342090 A342091 A342092 * A342094 A342095 A342096 KEYWORD nonn AUTHOR J. M. Bergot and Robert Israel, Feb 28 2021 STATUS approved

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Last modified August 4 13:04 EDT 2024. Contains 374921 sequences. (Running on oeis4.)