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A283556
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Digital root of the sum of the first n primes.
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1
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0, 2, 5, 1, 8, 1, 5, 4, 5, 1, 3, 7, 8, 4, 2, 4, 3, 8, 6, 1, 9, 1, 8, 1, 9, 7, 9, 4, 3, 4, 9, 1, 6, 8, 3, 8, 6, 1, 2, 7, 9, 8, 9, 2, 6, 5, 6, 1, 8, 1, 5, 4, 9, 7, 6, 2, 4, 3, 4, 2, 4, 8, 4, 5, 1, 8, 1, 8, 3, 8, 6, 8, 7, 5, 9, 1, 6, 8, 9, 5, 9, 5, 3, 2, 3, 1, 3, 2, 9, 2, 6, 5, 7, 8, 4, 8, 7, 3, 2, 3
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = ((A007504(n) - 1) mod 9) + 1.
a(n) = ((A051351(n) - 1) mod 9) + 1.
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EXAMPLE
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For n=3, a(3)=1 because the sum of the first 3 primes is 10 and the sum of digits of 10 is 1.
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MAPLE
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0, op(subs(0=9, ListTools:-PartialSums(select(isprime, [2, seq(i, i=3..1000, 2)])) mod 9)); # Robert Israel, Mar 30 2017
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MATHEMATICA
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With[{nn = 78}, {0}~Join~Table[NestWhile[Total@ IntegerDigits@ # &, #, # >= 10 &] &@ Total@ Take[#, n], {n, nn}] &@ Array[Prime, nn]] (* Michael De Vlieger, Mar 15 2017 *)
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PROG
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(PARI) {
p=0; print1(p", ");
forprime(n=2, 1000,
p+=n;
while(p>9, p=sumdigits(p))
; print1(p", ")
)
}
(Python)
from sympy import primerange
from itertools import accumulate
prime_sum = [0] + list(accumulate(primerange(2, 1000)))
def dig_root(n): return 1+(n-1)%9
def a(n):
return 0 if n<1 else dig_root(prime_sum[n])
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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