A075643
Group the natural numbers so that the n-th group contains n numbers one each of a multiple of numbers from 1 to n so that the group sum is a multiple of (n+1): (2), (1, 8), (3, 4, 9), (5, 6, 12, 32), (7, 10, 15, 16, 30), (11, 14, 18, 20, 25, 24), ... Sequence gives initial terms of groups.
Original entry on oeis.org
2, 1, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
Offset: 1
A076075
Final members of groups in A076077.
Original entry on oeis.org
2, 4, 6, 16, 25, 30, 42, 72, 63, 110, 132, 108, 247, 252, 240, 208, 493, 216, 437, 320, 483, 594, 552, 432, 650, 676, 540, 672, 928, 810, 899, 1088, 1023, 1190, 1155, 1080, 1332, 1064, 1638, 1720, 1722, 1554, 1935, 1980, 2025, 2208, 2162, 1728, 2303, 2400
Offset: 1
A076076
Primes associated with groups in A076077.
Original entry on oeis.org
2, 5, 17, 43, 79, 139, 197, 311, 433, 601, 823, 983, 1423, 1759, 2069, 2423, 3217, 3467, 4289, 4889, 5813, 6737, 7529, 8543, 9857, 11027, 12203, 13729, 15541, 17183, 18869, 21059, 22861, 25111, 27481, 29863, 32579, 35053, 38569, 41609, 44623, 47807
Offset: 1
A076077
Group the natural numbers so that the n-th group contains n numbers, the k-th number in a group is a multiple of k and the sum of the group is prime: (2), (1, 4), (3, 8, 6), (5, 10, 12, 16), (7, 14, 9, 24, 25), ...
Original entry on oeis.org
2, 1, 4, 3, 8, 6, 5, 10, 12, 16, 7, 14, 9, 24, 25, 11, 18, 15, 20, 45, 30, 13, 22, 21, 28, 35, 36, 42, 17, 26, 27, 32, 40, 48, 49, 72, 19, 34, 33, 44, 50, 54, 56, 80, 63, 23, 38, 39, 52, 55, 60, 70, 64, 90, 110, 29, 46, 51, 68, 65, 66, 77, 88, 81, 120, 132, 31, 58, 57, 76, 75
Offset: 1
2,
1, 4,
3, 8, 6,
5, 10, 12, 16,
7, 14, 9, 24, 25,
11, 18, 15, 20, 45, 30,
13, 22, 21, 28, 35, 36, 42,
17, 26, 27, 32, 40, 48, 49, 72,
19, 34, 33, 44, 50, 54, 56, 80, 63,
23, 38, 39, 52, 55, 60, 70, 64, 90,110,
29, 46, 51, 68, 65, 66, 77, 88, 81,120,132,
-
A076077 := proc(n,k)
option remember ;
local a,prev,nprev,kprev,psum;
for a from k by k do
prev := false ;
for nprev from 1 to n-1 do
for kprev from 1 to nprev do
if procname(nprev,kprev) = a then
prev := true ;
end if;
end do:
end do:
psum :=0 ;
for kprev from 1 to k-1 do
psum := psum+procname(n,kprev) ;
if procname(n,kprev) = a then
prev := true ;
end if;
end do:
if not prev then
if k = n-1 then
if igcd(a + psum,n) = 1 then
return a;
end if;
elif k = n then
if isprime(a + psum) then
return a;
end if;
else
return a;
end if;
end if;
end do:
end proc: # R. J. Mathar, Jul 08 2025
Showing 1-4 of 4 results.
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