A173252 A sequence of coefficients of 3^n when x_n = x_oi.

2, 1, 2, 19, 2, 289, 118, 41, 182578, 239803, 495074, 3866257, 1158454, 2629057, 56207062, 82084427, 4638842098, 5389722857, 30867186934, 8585039713, 5319558074, 2, 193589999521, 616960854422, 5663407855939, 5264528838038

Offset: 1

Author

A.K. Devaraj, Feb 14 2010

Keywords

• nonn
• uned
• obsc

Comments

The paper is not yet published - it can be furnished on request.

Sequence of x_n: 0, 3, 12, 39, 66, 795, 1524, 8085, 539526, 1070967, 2665290, ...

The x_n are given by recurrence x_(n+1) = x_n + 3^(s_n - 1), where s_n is the exponent of the highest power of 3 in v_n = x_n^2 + 18, and the a(n) are equal to v_n / 3^s_n.

References

• A. K. Devaraj, A theorem a la Ramanujan, Joint Meeting of AMS-BENELUX, '96.

Programs

PARI

lista(nn) = {x = 0; for (i=1, nn, y = x^2 + 18; s = valuation(y, 3); f = z^2 + 18; fx = subst(f, z, x); p3 = valuation (fx, 3); print1(fx/3^p3, ", "); x += 3^(s-1););} \\ Michel Marcus, Aug 08 2013

Extensions

More terms from Michel Marcus, Aug 08 2013