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Alois P. Heinz, <a href="/A173683/b173683.txt">Table of n, a(n) for n = 1..1000</a>
a(1) = 1 because (1 mod 2) = 1 where 2 = smallest prime >= 1.
seq (a(n), n=1..60); # _Alois P. Heinz_, Nov 25 2010
More terms and Maple program from Alois P. Heinz, Nov 25 2010
approved
editing
_Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), _, Nov 25 2010
More terms and Maple program from _Alois P. Heinz (heinz(AT)hs-heilbronn.de), _, Nov 25 2010
reviewed
approved
proposed
reviewed
a(1) = 1 because (1 mod 2) = 1 where 2 = smallest prime>=1.
a:= procn-> add (n mod ithprime(i), i=1..numtheory[pi] (nextprime(n-1))):
add (n mod ithprime(i), i=1..numtheory[pi] (nextprime(n-1)))
end:
seq (a (n), n=1..60);
Sum of remainders of n and prime(k), mod p, for prime(k)p=2, 3, 5, ..., smallest prime>=n.
1, 0, 1, 5, 3, 7, 4, 15, 14, 16, 14, 4, 8, 20, 13, 24, 23, 28, 18, 38, 27, 48, 47, 43, 29, 57, 62, 57, 64, 65, 46, 76, 56, 97, 95, 88, 88, 95, 70, 99, 96, 102, 74, 117, 88, 133, 140, 130, 98, 156, 165, 174, 170, 171, 134, 199, 200, 208, 203, 189, 147, 214
a:= proc(n)
add (n mod ithprime(i), i=1..numtheory[pi] (nextprime(n-1)))
end:
seq (a (n), n=1..60);
More terms and Maple program from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 25 2010
allocated Sum of remainders of n and prime(k), for Juri-Stepan Gerasimovprime(k)=2,3,5,...,smallest prime>=n.
1, 0, 1, 5, 3, 7, 4, 15, 16, 14, 4, 20, 13, 24, 23, 28, 18, 38
1,4
a(1)=1 because (1 mod 2)=1 where 2=smallest prime>1.
Cf. A099726.
allocated
nonn
Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 25 2010
approved
proposed