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 A033955 a(n) = sum of the remainders when the n-th prime is divided by primes up to the (n-1)-th prime. 12
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums of A207409. - Bob Selcoe, Apr 14 2014 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{k=1..n-1} ( prime(n) mod prime(k) ). EXAMPLE 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. MAPLE P:= [seq(ithprime(i), i=1..200)]: f:= proc(n) local j; add(P[n] mod P[j], j=1..n-1) end proc: map(f, [\$1..200]); # Robert Israel, Dec 29 2020 MATHEMATICA 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 *) PROG (PARI) {for(n=1, 200, print1(sum(k=1, n, prime(n)%prime(k)), ", "))} CROSSREFS Cf. A067435, A067436, A024934, A207409. Sequence in context: A153339 A275989 A343562 * A327466 A049720 A078172 Adjacent sequences: A033952 A033953 A033954 * A033956 A033957 A033958 KEYWORD nonn,easy AUTHOR Armand Turpel (armandt(AT)unforgettable.com) EXTENSIONS Edited by Dean Hickerson, Mar 02 2002 STATUS approved

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Last modified December 9 06:02 EST 2023. Contains 367685 sequences. (Running on oeis4.)