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A007605
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Sum of digits of n-th prime.
(Formerly M0633)
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89
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2, 3, 5, 7, 2, 4, 8, 10, 5, 11, 4, 10, 5, 7, 11, 8, 14, 7, 13, 8, 10, 16, 11, 17, 16, 2, 4, 8, 10, 5, 10, 5, 11, 13, 14, 7, 13, 10, 14, 11, 17, 10, 11, 13, 17, 19, 4, 7, 11, 13, 8, 14, 7, 8, 14, 11, 17, 10, 16, 11, 13, 14, 10, 5, 7, 11, 7, 13, 14, 16, 11, 17, 16, 13, 19, 14, 20, 19, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
CNRS press release, Sum of Digits of Prime Numbers Is Evenly Distributed: New Mathematical Proof of Hypothesis
Christian Mauduit, Joël Rivat, Sur un problème de Gelfond: la somme des chiffres des nombres premiers (French) [On a problem posed by Gelfond: the sum of digits of primes] Ann. of Math. (2) 171(2010), no. 3, 1591--1646. MR2680394 (2011j:11137)
R. G. Wilson, V, Letter to C. A. Pickover, Mar. 1993
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FORMULA
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a(n) = A007953(A000040(n)) = A007953(prime(n)).
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MAPLE
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map(t -> convert(convert(t, base, 10), `+`), select(isprime, [2, (2*i+1 $ i=1..1000)])); # Robert Israel, Aug 16 2015
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MATHEMATICA
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Table[Apply[Plus, RealDigits[Prime[n]][[1]]], {n, 1, 100}]
Plus@@ IntegerDigits[Prime[Range[100]]] (* Zak Seidov *)
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PROG
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(Magma) [ &+Intseq(NthPrime(n), 10): n in [1..80] ]; // Klaus Brockhaus, Jun 13 2009]
(PARI) dsum(n)=my(s); while(n, s+=n%10; n\=10); s
forprime(p=2, 1e3, print1(dsum(p)", ")) \\ Charles R Greathouse IV, Jul 15 2011
(PARI) a(n) = sumdigits(prime(n)); \\ Michel Marcus, Dec 20 2017
(Haskell)
a007605_list = map a007953 a000040_list -- Reinhard Zumkeller, Aug 04 2011
(Python)
from sympy import prime
def a(n): return sum(map(int, str(prime(n))))
print([a(n) for n in range(1, 80)]) # Michael S. Branicky, Feb 03 2021
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CROSSREFS
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Cf. A000040, A007953, A038194, A065073, A068395, A133223.
For inverse, see A067180 and A067523.
Sequence in context: A074463 A038194 A111309 * A077765 A078400 A068951
Adjacent sequences: A007602 A007603 A007604 * A007606 A007607 A007608
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
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STATUS
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approved
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