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 A309767 Approximation of the 2-adic integer arctanh(4) up to 2^n. 2
 0, 0, 0, 4, 4, 4, 4, 68, 196, 196, 708, 1732, 3780, 7876, 7876, 7876, 40644, 106180, 237252, 499396, 1023684, 1023684, 3120836, 7315140, 15703748, 15703748, 49258180, 116367044, 250584772, 250584772, 787455684, 787455684, 2934939332, 2934939332, 2934939332 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS arctanh(x) = x + x^3/3 + x^5/5 + x^7/7 + ... LINKS Table of n, a(n) for n=0..34. Wikipedia, p-adic number FORMULA a(n) = (Sum_{i=0..floor((n-3)/4)} 4^(2*i+1)/(2*i+1)) mod 2^n. EXAMPLE a(3) = 4^1 mod 2^3 = 4; a(6) = 4^1 mod 2^6 = 4 a(7) = (4^1 + 4^3/3) mod 2^7 = 68; a(10) = (4^1 + 4^3/3) mod 2^10 = 708; a(11) = (4^1 + 4^3/3 + 4^5/5) mod 2^11 = 1732; a(14) = (4^1 + 4^3/3 + 4^5/5) mod 2^14 = 7876; a(15) = (4^1 + 4^3/3 + 4^5/5 + 4^7/7) mod 2^15 = 7876. a(18) = (4^1 + 4^3/3 + 4^5/5 + 4^7/7) mod 2^18 = 237252. PROG (PARI) a(n) = lift(sum(i=0, (n-3)/4, Mod(4^(2*i+1)/(2*i+1), 2^n))) CROSSREFS Cf. A309753, A309756, A309768. Sequence in context: A309500 A321611 A309756 * A199500 A164838 A059112 Adjacent sequences: A309764 A309765 A309766 * A309768 A309769 A309770 KEYWORD nonn AUTHOR Jianing Song, Aug 16 2019 STATUS approved

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Last modified September 9 07:24 EDT 2024. Contains 375762 sequences. (Running on oeis4.)