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URL: https://oeis.org/A110638

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A110638
Every 2nd term of A083948 where the self-convolution 2nd power is congruent modulo 16 to A083948, which consists entirely of numbers 1 through 8.
2
1, 4, 2, 4, 7, 8, 4, 8, 3, 8, 2, 8, 1, 8, 8, 8, 6, 4, 6, 4, 6, 8, 4, 8, 4, 8, 2, 8, 8, 8, 8, 8, 7, 8, 6, 8, 8, 4, 6, 4, 8, 8, 6, 8, 7, 4, 8, 4, 3, 4, 4, 4, 3, 8, 6, 8, 3, 8, 8, 8, 1, 8, 4, 8, 4, 8, 8, 8, 3, 8, 6, 8, 6, 8, 2, 8, 5, 8, 8, 8, 1, 8, 4, 8, 6, 4, 4, 4, 6, 8, 6, 8, 1, 4, 8, 4, 1, 8, 6, 8, 5, 4, 8, 4, 4
OFFSET
0,2
EXAMPLE
A(x) = 1 + 4*x + 2*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 4*x^6 +...
A(x)^2 = 1 + 8*x + 20*x^2 + 24*x^3 + 50*x^4 + 88*x^5 +...
A(x)^2 (mod 16) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 +...
G(x) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 + 4*x^6 +...
where G(x) is the g.f. of A083948.
PROG
(PARI) {a(n)=local(d=2, m=8, 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)}
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved