A007605 Sum of digits of n-th prime.
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
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- 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 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)
- Enrique Navarrete, Distributions of Sums of Digits of Primes
- Robert G. Wilson v, Letter to C. A. Pickover, Mar. 1993
Crossrefs
Programs
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Haskell
a007605_list = map a007953 a000040_list -- Reinhard Zumkeller, Aug 04 2011
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Magma
[ &+Intseq(NthPrime(n), 10): n in [1..80] ]; // Klaus Brockhaus, Jun 13 2009
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Maple
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
Table[Apply[Plus, RealDigits[Prime[n]][[1]]], {n, 1, 100}] Plus@@ IntegerDigits[Prime[Range[100]]] (* Zak Seidov *) -
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
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PARI
a(n) = sumdigits(prime(n)); \\ Michel Marcus, Dec 20 2017
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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