A059877 -id:A059877 - cp's OEIS frontend

A059876 a(n) = bin_prime_sum(n).

2, 1, 3, 3, 5, 7, 9, -1, 1, 3, 5, 5, 7, 9, 11, 3, 5, 7, 9, 9, 11, 13, 15, 13, 15, 17, 19, 19, 21, 23, 25, -7, -5, -3, -1, -1, 1, 3, 5, 3, 5, 7, 9, 9, 11, 13, 15, 7, 9, 11, 13, 13, 15, 17, 19, 17, 19, 21, 23, 23, 25, 27, 29, -3, -1, 1, 3, 3, 5, 7, 9, 7, 9, 11, 13, 13, 15, 17, 19, 11, 13, 15, 17, 17, 19, 21, 23, 21, 23, 25, 27, 27, 29, 31, 33, 19, 21, 23, 25, 25, 27, 29, 31, 29, 31

Offset: 1

Antti Karttunen, Feb 05 2001

sign

From R. J. Mathar, Nov 12 2011: (Start)
The function bin_prime_sum of an argument n is a sum of three numbers. Let s = A000523(n) be the exponent of the largest power of 2 less than or equal to n and prime=A000040. Then the three terms are:
i) (-1)^(n+1);
ii) sum_{i=1..s} prime(i) * (1 + (-1)^[n/2^i] ); where [..] is the floor bracket;
iii) 1 (if n=1), otherwise prime(s) (if s even) or 0 (if s odd). (End)

Cf. A059871, A059872, A059873, A059877, A059878, A059880.

with(numtheory); bin_prime_sum := proc(n) local i,s; s := floor_log_2(n); RETURN(((-1)^(n+1)) + add( (((-1)^(floor(n/(2^i))+1))*ithprime(i)),i=1..s) + (`if`((1 = n),1,((`mod`((s+1),2))*ithprime(s)))) ); end;

a[n_] := With[{s = Floor[Log[2, n]]}, (-1)^(n+1) + Sum[(-1)^(Floor[n/2^i] + 1)*Prime[i], {i, 1, s}] + If[1 == n, 1, Mod[s+1, 2]*Prime[s]]]; Array[a, 105] (* Jean-François Alcover, Mar 07 2016, adapted from Maple *)

a(A059873(n)) = A000040(n).

A059879 Those n for which the absolute value of A059878[n] is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 16, 18, 20, 21, 24, 27, 31, 34, 37, 39, 41, 43, 46, 47, 48, 50, 51, 53, 54, 55, 57, 60, 61, 65, 67, 68, 71, 78, 83, 84, 86, 87, 101, 103, 105, 106, 109, 112, 114, 117, 126, 127, 128, 129, 141, 143, 145, 154, 155, 158, 161, 168, 179, 181

Offset: 1

Antti Karttunen, Feb 05 2001

nonn

Of the first 511 terms of A059878, 128 are primes.

Cf. A059877.

positions(true,map(isprime,map(abs, A059878))); # positions function given in A059649.

cp's OEIS Frontend

A059876 a(n) = bin_prime_sum(n).

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