A231532 Decimal expansion of the real part of Sum_{n=0..inf}(1/c_n), c_0=1, c_n=c_(n-1)*(n+I).

1, 5, 9, 1, 5, 4, 7, 8, 1, 4, 7, 3, 2, 8, 5, 1, 9, 5, 7, 3, 3, 6, 7, 7, 9, 8, 8, 2, 0, 6, 4, 9, 9, 8, 2, 7, 6, 2, 4, 6, 0, 5, 9, 2, 6, 7, 4, 7, 8, 6, 8, 0, 0, 9, 2, 5, 4, 5, 3, 5, 3, 2, 5, 7, 0, 7, 6, 3, 8, 0, 1, 6, 3, 3, 1, 5, 2, 7, 1, 6, 6, 4, 8, 8, 3, 7, 0, 3, 2, 6, 8, 6, 9, 6, 8, 5, 9, 6, 3, 4, 5, 4, 8, 8, 9

Offset

1,2

Comments

Consider an extension of exp(x) to an intriguing function, expim(x,y), defined by the power series Sum_{n=0..inf}(x^n/c_n), where c_0 = 1, c_n = c_(n-1)*(n+y*I), so that exp(x) = expim(x,0). The current sequence regards the real part of expim(1,1). The decimal expansion of the imaginary part is in A231533 and that of the absolute value in A231534.

Links

Stanislav Sykora, Table of n, a(n) for n = 1..10000

Formula

real(Sum_{n=0..inf}(1/(A231530(n)+A231531(n)*I))).

Example

1.59154781473285195733677988...

Prog

(PARI) Expim(x, y)={local (c, k, lastval, val); c = 1.0+0.0*I; lastval = c; k = 1; while (k, c*=x/(k + y*I); val = lastval + c; if (val==lastval, break);   lastval = val; k += 1; ); return (val); }
real(Expim(1, 1))

Crossrefs

Cf. A231533 (imaginary part), A231534 (absolute value), and A231530, A231531 (respectively, the real and imaginary parts of the expansion coefficient's denominators).

Sequence in context: A274418 A127414 A186192 * A086201 A362742 A010490

Adjacent sequences: A231529 A231530 A231531 * A231533 A231534 A231535

Keyword

nonn,cons

Author

Stanislav Sykora, Nov 10 2013

Status

approved