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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A136392 a(n) = 6*n^2 - 10*n + 5.

Original entry on oeis.org

1, 9, 29, 61, 105, 161, 229, 309, 401, 505, 621, 749, 889, 1041, 1205, 1381, 1569, 1769, 1981, 2205, 2441, 2689, 2949, 3221, 3505, 3801, 4109, 4429, 4761, 5105, 5461, 5829, 6209, 6601, 7005, 7421, 7849, 8289, 8741, 9205, 9681, 10169, 10669, 11181, 11705, 12241
Offset: 1

Views

Author

Gary W. Adamson, Dec 28 2007

Keywords

Comments

Binomial transform of [1, 8, 12, 0, 0, 0, ...].
Numbers k such that 6*k - 5 is the square of a number of the form 6*k - 5, contained in A199859. - Eleonora Echeverri-Toro, Nov 29 2011
Central terms of the triangle A033292. - Reinhard Zumkeller, Feb 06 2012
Sequence found by reading the line from 1, in the direction 1, 9, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Jul 18 2012

Links

Crossrefs

Cf. A000567, A001318, A016777, A033292, A033580, A059722, A199859, A201279, A204675.

Programs

Formula

a(n) = n*(3*n - 2) + (n-1)*(3*n - 5), n > 1.
a(n) = n*A016777(n-1) + (n-1)*A016777(n-2).
a(n) = a(n-1) + 12*n - 16 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010
G.f.: x*(1+x)*(1+5*x)/(1-x)^3. - Colin Barker, Jan 09 2012
a(n) = 1 + A033580(n-1). - Omar E. Pol, Jul 18 2012
a(n) = A059722(n) - A059722(n-1). - J. M. Bergot, Nov 02 2012
a(n) = A000567(n-1) + A000567(n). - Charlie Marion, May 29 2024
From Elmo R. Oliveira, Oct 31 2024: (Start)
E.g.f.: exp(x)*(2*x*(3*x - 2) + 5) - 5.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

A199860 Numbers k such that 6k-5 is a composite number of the form (6x-1) * (6y-1).

Original entry on oeis.org

5, 10, 15, 20, 21, 25, 30, 32, 35, 40, 43, 45, 49, 50, 54, 55, 60, 65, 66, 70, 75, 76, 80, 83, 85, 87, 89, 90, 95, 98, 100, 105, 109, 110, 112, 115, 117, 120, 125, 130, 131, 134, 135, 140, 141, 142, 145, 150, 151, 153, 155, 158, 160, 164, 165, 168, 170, 175
Offset: 1

Views

Author

Eleonora Echeverri-Toro, Nov 11 2011

Keywords

Comments

Numbers whose associate in A091300 has at least one factorization into two factors of A016969.

Examples

			n=5 is in the sequence because 6*5-5 = 25 = 5*5 with x = y = 1.
n=10 is in the sequence because 6*10-5 = 55 = 5*11 with x=1, y=2.

Crossrefs

Cf. A199859.

Programs

  • Maple
    isA016969 := proc(n)
    (n mod 6)=5 ;
end proc:
isA016921 := proc(n)
    (n mod 6)=1 ;
end proc:
isA091300 := proc(n)
    (not isprime(n)) and isA016921(n) ;
end proc:
isA199860 := proc(n)
    if isA091300(6*n-5) then
        for d in numtheory[divisors](6*n-5) minus {1} do
            if isA016969(d) and isA016969((6*n-5)/d) then
                return true;
            end if;
        end do:
        return false;
    else
        return false;
    end if;
end proc:
for n from 5 to 210 do
    if isA199860(n) then
        printf("%d,",n) ;
    end if ;
end do; # R. J. Mathar, Nov 27 2011
Showing 1-2 of 2 results.

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