

A049882


a(n) is the number of distinct sums of 4 different primes chosen from the first n primes.


3



1, 5, 13, 23, 32, 43, 57, 69, 84, 98, 110, 125, 139, 155, 170, 187, 202, 214, 230, 246, 262, 281, 299, 316, 330, 344, 357, 379, 401, 420, 437, 459, 477, 495, 515, 534, 553, 571, 586, 608, 627, 642, 657, 677, 701, 725, 748, 767, 783, 801, 821, 841, 859, 876, 900, 917, 935, 949, 970, 997
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OFFSET

4,2


LINKS

Table of n, a(n) for n=4..63.


EXAMPLE

From Petros Hadjicostas, Nov 19 2019: (Start)
The first 4 primes are 2, 3, 5, and 7 and they form only one sum, so a(4) = 1.
The first 5 primes are 2, 3, 5, 7, and 11, and they form 5 distinct sums each with four different terms (17, 21, 23, 25, 26), so a(2) = 5.
The first 6 primes are 2, 3, 5, 7, 11, and 13, and they form 13 distinct sums each with four different terms (17, 21, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36), so a(6) = 13. (End)


MAPLE

f := proc(n) local v, i, j, k, m; v := {};
if 4 <= n then
for i from 1 to n  3 do
for j from i + 1 to n  2 do
for k from j + 1 to n  1 do
for m from k + 1 to n do
v := v union {ithprime(i) + ithprime(j) + ithprime(k) + ithprime(m)};
end do; end do; end do; end do;
end if; nops(v); end proc;
seq(f(n), n=4..40); # Petros Hadjicostas, Nov 19 2019


CROSSREFS

Cf. A000040, A049880, A049881, A253250.
Sequence in context: A143988 A129806 A125830 * A108195 A074798 A031336
Adjacent sequences: A049879 A049880 A049881 * A049883 A049884 A049885


KEYWORD

nonn


AUTHOR

Clark Kimberling


EXTENSIONS

Name edited by and more terms from Petros Hadjicostas, Nov 19 2019


STATUS

approved



