cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A309903 Approximation of the 5-adic integer exp(-5) up to 5^n.

Original entry on oeis.org

0, 1, 21, 71, 196, 2071, 2071, 33321, 345821, 736446, 8548946, 18314571, 18314571, 994877071, 994877071, 25408939571, 86444095821, 239031986446, 1001971439571, 16260760502071, 92554705814571, 283289569095821, 1236963885502071, 8389521258548946
Offset: 0

Views

Author

Jianing Song, Aug 21 2019

Keywords

Comments

In p-adic field, the exponential function exp(x) is defined as Sum_{k>=0} x^k/k!. When extended to a function over the metric completion of the p-adic field, exp(x) has radius of convergence p^(-1/(p-1)) (i.e., exp(x) converges for x such that |x|_p < p^(-1/(p-1)), where |x|_p is the p-adic metric). As a result, for odd primes p, exp(p) is well-defined in p-adic field, and exp(4) is well defined in 2-adic field.
a(n) is the multiplicative inverse of A309902(n) modulo 5^n.

Links

Crossrefs

Cf. A309902.
The 5-adic expansion of exp(5) is given by A309975.
Approximations of exp(-p) in p-adic field: A309901 (p=3), this sequence (p=5), A309905 (p=7).

Programs

  • PARI
    a(n) = lift(exp(-5 + O(5^n)))

A309905 Approximation of the 7-adic integer exp(-7) up to 7^n.

Original entry on oeis.org

0, 1, 43, 190, 1562, 6364, 56785, 645030, 3115659, 14645261, 14645261, 297120510, 8206427482, 22047714683, 118936725090, 118936725090, 23856744274805, 123555535983608, 588816563958022, 5474057357689369, 51069638099181941, 51069638099181941
Offset: 0

Views

Author

Jianing Song, Aug 21 2019

Keywords

Comments

In p-adic field, the exponential function exp(x) is defined as Sum_{k>=0} x^k/k!. When extended to a function over the metric completion of the p-adic field, exp(x) has radius of convergence p^(-1/(p-1)) (i.e., exp(x) converges for x such that |x|_p < p^(-1/(p-1)), where |x|_p is the p-adic metric). As a result, for odd primes p, exp(p) is well-defined in p-adic field, and exp(4) is well defined in 2-adic field.
a(n) is the multiplicative inverse of A309904(n) modulo 7^n.

Links

Crossrefs

Cf. A309904.
The 7-adic expansion of exp(-7) is given by A309988.
Approximations of exp(-p) in p-adic field: A309901 (p=3), A309903 (p=5), this sequence (p=7).

Programs

  • PARI
    a(n) = lift(exp(-7 + O(7^n)))

A309900 Approximation of the 3-adic integer exp(3) up to 3^n.

Original entry on oeis.org

0, 1, 4, 13, 67, 229, 229, 958, 958, 7519, 27202, 27202, 204349, 1267231, 1267231, 10833169, 39530983, 125624425, 125624425, 125624425, 1287885892, 4774670293, 15235023496, 46616083105, 140759261932, 140759261932, 988047871375, 3529913699704, 11155511184691
Offset: 0

Views

Author

Jianing Song, Aug 21 2019

Keywords

Comments

In p-adic field, the exponential function exp(x) is defined as Sum_{k>=0} x^k/k!. When extended to a function over the metric completion of the p-adic field, exp(x) has radius of convergence p^(-1/(p-1)) (i.e., exp(x) converges for x such that |x|_p < p^(-1/(p-1)), where |x|_p is the p-adic metric). As a result, for odd primes p, exp(p) is well-defined in p-adic field, and exp(4) is well defined in 2-adic field.
a(n) is the multiplicative inverse of A309901(n) modulo 3^n.

Links

Crossrefs

Cf. A309901.
The 3-adic expansion of exp(3) is given by A317675.
Approximations of exp(p) in p-adic field: this sequence (p=3), A309902 (p=5), A309904 (p=7).

Programs

  • PARI
    a(n) = lift(exp(3 + O(3^n)))
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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