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A007605
Sum of digits of n-th prime.
(Formerly M0633)
91
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
OFFSET
1,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Christian Mauduit and 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)
FORMULA
a(n) = A007953(A000040(n)) = A007953(prime(n)).
MAPLE
map(t -> convert(convert(t, base, 10), `+`), select(isprime, [2, (2*i+1 $ i=1..1000)])); # Robert Israel, Aug 16 2015
MATHEMATICA
Table[Apply[Plus, RealDigits[Prime[n]][[1]]], {n, 1, 100}]
Plus@@ IntegerDigits[Prime[Range[100]]] (* Zak Seidov *)
PROG
(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
CROSSREFS
For inverse, see A067180 and A067523.
Sequence in context: A074463 A038194 A111309 * A077765 A078400 A068951
KEYWORD
nonn,base,easy
STATUS
approved