A110647 -id:A110647 - cp's OEIS frontend

A110649 Every 2nd term of A084067 where the self-convolution 2nd power is congruent modulo 8 to A084067, which consists entirely of numbers 1 through 12.

1, 6, 9, 4, 12, 6, 6, 12, 12, 8, 9, 12, 12, 6, 6, 10, 6, 12, 2, 6, 6, 12, 12, 12, 8, 12, 3, 4, 12, 12, 9, 6, 6, 4, 12, 12, 2, 6, 3, 6, 3, 6, 7, 6, 9, 8, 9, 12, 12, 12, 3, 12, 3, 6, 2, 6, 12, 2, 6, 6, 3, 12, 9, 4, 3, 12, 4, 12, 6, 2, 3, 12, 9, 6, 6, 6, 3, 6, 10, 6, 6, 6, 9, 6, 12, 12, 9, 2, 12, 6, 9

Offset: 0

Robert G. Wilson v and Paul D. Hanna, Aug 30 2005

nonn

			A(x) = 1 + 6*x + 9*x^2 + 4*x^3 + 12*x^4 + 6*x^5 +...
A(x)^2 = 1 + 12*x + 54*x^2 + 116*x^3 + 153*x^4 + 228*x^5 +...
A(x)^2 (mod 8) = 1 + 4*x + 6*x^2 + 4*x^3 + x^4 + 4*x^5 +...
G(x) = 1 + 12*x + 6*x^2 + 4*x^3 + 9*x^4 + 12*x^5 + 4*x^6 +...
where G(x) is the g.f. of A084067.

Cf. A084067, A110645, A110646, A110647, A110648.

{a(n)=local(d=2,m=12,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break)));polcoeff(A,d*n)}

A110645 Every 12th term of A084067.

Original entry on oeis.org

1, 6, 12, 2, 8, 9, 2, 7, 12, 2, 3, 4, 9, 10, 12, 9, 2, 5, 12, 9, 8, 10, 1, 9, 7, 2, 9, 4, 11, 1, 10, 5, 4, 1, 12, 2, 9, 4, 5, 11, 12, 12, 9, 5, 12, 5, 3, 12, 1, 4, 6, 2, 10, 11, 5, 1, 6, 10, 12, 9, 11, 9, 9, 5, 3, 3, 7, 2, 6, 7, 5, 9, 5, 10, 12, 5, 5, 4, 4, 2, 1, 8, 7, 11, 7, 6, 1, 2, 5, 10, 9, 8, 9, 9

Offset: 0

Robert G. Wilson v and Paul D. Hanna, Aug 30 2005

nonn

Cf. A084067, A110646, A110647, A110648, A110649.

{a(n)=local(d=12,m=12,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break)));polcoeff(A,d*n)}

A110646 Every 6th term of A084067.

Original entry on oeis.org

1, 4, 6, 8, 12, 10, 2, 12, 8, 4, 9, 4, 2, 6, 7, 8, 12, 12, 2, 2, 3, 4, 4, 2, 9, 6, 10, 6, 12, 2, 9, 10, 2, 2, 5, 6, 12, 2, 9, 8, 8, 8, 10, 8, 1, 4, 9, 10, 7, 10, 2, 6, 9, 10, 4, 8, 11, 2, 1, 4, 10, 2, 5, 2, 4, 2, 1, 8, 12, 2, 2, 12, 9, 2, 4, 4, 5, 8, 11, 4, 12, 4, 12, 6, 9, 12, 5, 6, 12, 10, 5, 12, 3

Offset: 0

Robert G. Wilson v and Paul D. Hanna, Aug 30 2005

nonn

Cf. A084067, A110645, A110647, A110648, A110649.

{a(n)=local(d=6,m=12,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break)));polcoeff(A,d*n)}

A110648 Every third term of A084067 where the self-convolution third power is congruent modulo 9 to A084067, which consists entirely of numbers 1 through 12.

Original entry on oeis.org

1, 4, 4, 8, 6, 12, 8, 12, 12, 12, 10, 12, 2, 8, 12, 4, 8, 8, 4, 4, 9, 4, 4, 12, 2, 12, 6, 8, 7, 4, 8, 12, 12, 8, 12, 8, 2, 8, 2, 8, 3, 12, 4, 12, 4, 12, 2, 12, 9, 12, 6, 12, 10, 8, 6, 12, 12, 12, 2, 8, 9, 12, 10, 12, 2, 8, 2, 4, 5, 4, 6, 12, 12, 8, 2, 12, 9, 4, 8, 4, 8, 12, 8, 4, 10, 8, 8, 12, 1, 12

Offset: 0

Robert G. Wilson v and Paul D. Hanna, Aug 30 2005

nonn

			A(x) = 1 + 4*x + 4*x^2 + 8*x^3 + 6*x^4 + 12*x^5 +...
A(x)^3 = 1 + 12*x + 60*x^2 + 184*x^3 + 450*x^4 + 948*x^5 +...
A(x)^3 (mod 9) = 1 + 3*x + 6*x^2 + 4*x^3 + 3*x^5 + 4*x^6 +...
G(x) = 1 + 12*x + 6*x^2 + 4*x^3 + 9*x^4 + 12*x^5 + 4*x^6 +...
where G(x) is the g.f. of A084067.

Cf. A084067, A110645, A110646, A110647, A110649.

{a(n)=local(d=3,m=12,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break)));polcoeff(A,d*n)}

cp's OEIS Frontend

A110649 Every 2nd term of A084067 where the self-convolution 2nd power is congruent modulo 8 to A084067, which consists entirely of numbers 1 through 12.

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A110645 Every 12th term of A084067.

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A110646 Every 6th term of A084067.

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A110648 Every third term of A084067 where the self-convolution third power is congruent modulo 9 to A084067, which consists entirely of numbers 1 through 12.

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PARI