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 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). 3
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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 A010490 A021173 Adjacent sequences:  A231529 A231530 A231531 * A231533 A231534 A231535 KEYWORD nonn,cons AUTHOR Stanislav Sykora, Nov 10 2013 STATUS approved

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Last modified August 14 09:05 EDT 2018. Contains 313750 sequences. (Running on oeis4.)