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A316434
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a(n) = a(pi(n)) + a(n-pi(n)) with a(1) = a(2) = 1.
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5
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1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 11, 12, 12, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 21, 22, 22, 22, 23, 23, 24, 25, 25, 25, 26, 27, 28, 28, 29, 30, 31, 31, 32, 32, 33, 33, 34, 35, 35, 35, 36, 36, 37, 38, 39, 39, 39, 40, 41, 42, 42, 42, 43, 44, 44
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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This sequence hits every positive integer.
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LINKS
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FORMULA
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a(n+1) - a(n) = 0 or 1 for all n >= 1.
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MAPLE
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f:= proc(n) option remember: local p;
p:= numtheory:-pi(n);
procname(p) + procname(n-p)
end proc:
f(1):= 1: f(2):= 1:
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MATHEMATICA
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a[1]=a[2]=1; a[n_] := a[n] = a[PrimePi[n]] + a[n - PrimePi[n]]; Array[a, 75] (* Giovanni Resta, Nov 02 2018 *)
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PROG
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(PARI) q=vector(75); for(n=1, 2, q[n] = 1); for(n=3, #q, q[n] = q[primepi(n)] + q[n-primepi(n)]); q
(C++) See Links section.
(Python)
from sympy import primepi
pp = primepi(n)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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