Samuel J. Erickson has authored 2 sequences.
Original entry on oeis.org
10, 21, 44, 75, 104, 157, 230, 283, 372, 529, 602, 739, 938, 1011, 1292, 1521, 1521, 1648, 2031, 2260, 2409, 2798, 3261, 3454, 3813, 4360, 4599, 5066, 5889, 6068
Offset: 2
The second term is obtained by taking the trace of the matrix [[3,5,11],[3,7,13],[5,7,11]].
-
Primes:= select(isprime,{seq(2*i+1,i=1..10^5)}):
T:= 3:
for n from 2 to 100 do
R:= Primes intersect map(`+`,Primes, -2*n);
if nops(R) < n then break fi;
T:= T + R[n];
A[n]:= T;
od:
seq(A[n],n=2..100); # Robert Israel, Aug 06 2014
A240986
Determinants of n X n matrices of sets of distinct primes selected by increasing prime gaps (see comments).
Original entry on oeis.org
3, 6, -36, -216, 1296, -5184, -145152, -3856896, -170325504, -6133211136, 1094593056768, 26742290558976, -497681937801216, -14357497419546624, 657148066947072000, 12008320398059765760, 1322255096225695531008, 70546799432003423698944, -6537119853797882157072384, -27940593871362459110473728
Offset: 1
For the first element of the sequence we find the determinant of the matrix [[3,5],[3,7]], where [3,5] is row 1 and [3,7] is row 2. These numbers are there because in row 1 we are looking at the primes where we can add 2 to get another prime; 3+2 is prime and so is 5+2, so they go in row 1. Similarly, for the second row we get [3,7] because these are the first primes such that when 4 is added we get a prime: 3+4 and 7+4 are both prime, so they go in row 2. For the second entry in the sequence we take the determinant of [[3,5,11],[3,7,13],[5,7,11]]; the reason we get [5,7,11] in the third row is because 5 is the first prime where 5+6 is prime, 7 is second prime where 7+6 is prime, and 11 is the third prime where 11+6 is prime.
-
a(n) = {my(m=matrix(n,n), j); for (i=1, n, j = 1; forprime(p=2, , if (isprime(p+2*i), m[i,j] = p; j++); if (j > n, break););); matdet(m);} \\ Michel Marcus, May 04 2019
-
# See Erickson link.
Comments