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A033955
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a(n) = sum of the remainders when the n-th prime is divided by primes up to the (n-1)-th prime.
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12
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0, 1, 3, 4, 8, 13, 18, 27, 29, 46, 56, 70, 74, 88, 98, 134, 147, 171, 200, 217, 252, 274, 309, 323, 348, 418, 448, 471, 522, 571, 629, 685, 739, 777, 793, 853, 954, 997, 1002, 1120, 1148, 1220, 1338, 1419, 1466, 1540, 1615, 1573, 1633, 1707, 1825, 1892, 1986
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n-1} ( prime(n) mod prime(k) ).
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EXAMPLE
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a(5) = 8. The remainders when the fifth prime 11 is divided by 2, 3, 5, 7 are 1, 2, 1, 4, respectively and their sum = 8.
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MAPLE
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P:= [seq(ithprime(i), i=1..200)]:
f:= proc(n) local j; add(P[n] mod P[j], j=1..n-1) end proc:
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MATHEMATICA
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a[n_] := Sum[Mod[Prime[n], Prime[i]], {i, 1, n-1}]
Table[Total[Mod[Prime[n], Prime[Range[n-1]]]], {n, 60}] (* Harvey P. Dale, Mar 07 2018 *)
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PROG
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(PARI) {for(n=1, 200, print1(sum(k=1, n, prime(n)%prime(k)), ", "))}
(Python) from sympy import prime; {print(sum(prime(n)%prime(k) for k in range(1, n)), end =', ') for n in range(1, 54)} # Ya-Ping Lu, May 05 2024
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Armand Turpel (armandt(AT)unforgettable.com)
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EXTENSIONS
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STATUS
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approved
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