A007605 Sum of digits of n-th prime. (Formerly M0633)

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

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

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

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

Keyword

nonn,base

Author

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

Status

approved