A249447 -id:A249447 - cp's OEIS frontend

A279437 Number of ways to place 3 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

0, 4, 78, 528, 2200, 6900, 17934, 40768, 83808, 159300, 284350, 482064, 782808, 1225588, 1859550, 2745600, 3958144, 5586948, 7739118, 10541200, 14141400, 18711924, 24451438, 31587648, 40380000, 51122500, 64146654, 79824528, 98571928, 120851700, 147177150, 178115584

Offset: 1

Heinrich Ludwig, Dec 12 2016

Column 4 of triangle A279445.
Rotations and reflections of placements are counted. For numbers if they are to be ignored see A279447.
For condition "no more than 2 points on straight lines at any angle", see A045996.

Heinrich Ludwig, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A045996, A249447, A279444, A279445, A197458.

Same problem but 2, 4..9 points: A083374, A279438, A279439, A279440, A279441, A279442, A279443.

Table[(n^6 - 5 n^4 + 6 n^3 - 2 n^2)/6, {n, 32}] (* or *)
Rest@ CoefficientList[Series[2 x^2*(2 + 25 x + 33 x^2 + x^3 - x^4)/(1 - x)^7, {x, 0, 32}], x] (* Michael De Vlieger, Dec 12 2016 *)

concat(0, Vec(2*x^2*(2 + 25*x + 33*x^2 + x^3 - x^4) / (1 - x)^7 + O(x^50))) \\ Colin Barker, Dec 12 2016

a(n) = (n^6 - 5*n^4 + 6*n^3 - 2*n^2)/6.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
G.f.: 2*x^2*(2 + 25*x + 33*x^2 + x^3 - x^4) / (1 - x)^7. - Colin Barker, Dec 12 2016

A249448 Largest n-digit prime whose digit sum is also prime.

Original entry on oeis.org

7, 89, 991, 9967, 99991, 999983, 9999971, 99999989, 999999937, 9999999943, 99999999821, 999999999989, 9999999999971, 99999999999923, 999999999999883, 9999999999999851, 99999999999999997, 999999999999999967, 9999999999999999919, 99999999999999999989, 999999999999999999829

Offset: 1

Paolo P. Lava, Oct 29 2014

Subsequence of A046704 (primes with digit sum being prime).

Some terms of this sequence are also in A003618, the largest n-digit primes.

			a(1) = 7 because it is the largest prime with just one digit.
a(2) = 89 because it is the largest prime with 2 digits whose sum, 8 + 9 = 17, is a prime.
Again, a(7) = 9999971 because it is the largest prime with 7 digits whose sum is a prime: 9 + 9 + 9 + 9 + 9 + 7 + 1 = 53.

Paolo P. Lava, Table of n, a(n) for n = 1..100

Cf. A046704, A103545, A249447.

P:=proc(q) local a,b,k,n; for k from 0 to q do
for n from 10^(k+1)-1 by -1 to 10^k do if isprime(n) then a:=n; b:=0;
while a>0 do b:=b+(a mod 10); a:=trunc(a/10); od;
if isprime(b) then print(n); break; fi; fi;
od; od; end: P(10^3);

Table[Module[{p=NextPrime[10^n,-1]},While[!PrimeQ[Total[IntegerDigits[p]]],p=NextPrime[p,-1]];p],{n,25}] (* Harvey P. Dale, Jun 20 2023 *)

a(n) = {p = precprime(10^n); while (!isprime(sumdigits(p)), p = precprime(p-1)); p;} \\ Michel Marcus, Oct 29 2014

cp's OEIS Frontend

A279437 Number of ways to place 3 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

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