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 A007468 Sum of next n primes. (Formerly M1846) 19
 2, 8, 31, 88, 199, 384, 659, 1056, 1601, 2310, 3185, 4364, 5693, 7360, 9287, 11494, 14189, 17258, 20517, 24526, 28967, 33736, 38917, 45230, 51797, 59180, 66831, 75582, 84463, 95290, 106255, 117424, 129945, 143334, 158167, 173828, 190013, 207936, 225707, 245724 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If we arrange the prime numbers into a triangle, with 2 at the top, 3 and 5 in the second row, 7, 11 and 13 in the third row, and so on and so forth, this sequence gives the row sums. - Alonso del Arte, Nov 08 2011 In the first 20000 terms, the only perfect square > 1 is 207936 (n=38). Is it the only one? Is there some proof/conjecture? - Carlos Eduardo Olivieri, Mar 09 2015 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 FORMULA a(n) = prime(1 + n(n-1)/2) + ... + prime(n + n(n-1)/2), where prime(i) is i-th prime. EXAMPLE a(1)=2 because "sum of next 1 prime" is 2; a(2)=8 because sum of next 2 primes is 3+5=8; a(3)=31 because sum of next 3 primes is 7+11+13=31, etc. MATHEMATICA a[n_] := Sum[Prime[i], {i, 1+n(n-1)/2, n+n(n-1)/2}]; Table[a[n], {n, 100}] With[{nn=40}, Total/@TakeList[Prime[Range[(nn(nn+1))/2]], Range[nn]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jan 15 2020 *) PROG (Python) from sympy import nextprime def aupton(terms):   alst, p = [], 2   for n in range(1, terms+1):     s = 0     for i in range(n):       s += p       p = nextprime(p)     alst.append(s)   return alst print(aupton(40)) # Michael S. Branicky, Feb 08 2021 CROSSREFS Cf. A078721 and A011756 for the starting and ending prime of each sum. Sequence in context: A266043 A265950 A294264 * A280156 A054137 A343414 Adjacent sequences:  A007465 A007466 A007467 * A007469 A007470 A007471 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Zak Seidov, Sep 21 2002 STATUS approved

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Last modified October 2 23:51 EDT 2022. Contains 357230 sequences. (Running on oeis4.)