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.

A309904 Approximation of the 7-adic integer exp(7) up to 7^n.

Original entry on oeis.org

0, 1, 8, 204, 890, 890, 51311, 286609, 3580781, 20875184, 182289612, 747240110, 8656547082, 8656547082, 105545557489, 783768630338, 15026453160167, 114725244868970, 1045247300817798, 9187315290370043, 20586210475743186, 20586210475743186
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 A309905(n) modulo 7^n.

Links

Crossrefs

Cf. A309905.
The 7-adic expansion of exp(7) is given by A309987.
Approximations of exp(p) in p-adic field: A309900 (p=3), A309902 (p=5), this sequence (p=7).

Programs

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

A309901 Approximation of the 3-adic integer exp(-3) up to 3^n.

Original entry on oeis.org

0, 1, 7, 25, 52, 52, 538, 1267, 1267, 1267, 20950, 20950, 198097, 1260979, 1260979, 6043948, 6043948, 92137390, 92137390, 866978368, 2029239835, 5516024236, 26436730642, 57817790251, 246104147905, 810963220867, 1658251830310, 6741983486968, 21993178456942
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 A309900(n) modulo 3^n.

Links

Crossrefs

Cf. A309900.
The 3-adic expansion of exp(-3) is given by A309866.
Approximations of exp(-p) in p-adic field: this sequence (p=3), A309903 (p=5), A309905 (p=7).

Programs

  • PARI
    a(n) = lift(exp(-3 + O(3^n)))

A309902 Approximation of the 5-adic integer exp(5) up to 5^n.

Original entry on oeis.org

0, 1, 6, 81, 456, 2956, 6081, 37331, 349831, 1521706, 3474831, 3474831, 101131081, 833552956, 4495662331, 16702693581, 16702693581, 169290584206, 1695169490456, 16953958552956, 55100931209206, 436570657771706, 2343919290584206, 9496476663631081
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 A309903(n) modulo 5^n.

Links

Crossrefs

Cf. A309903.
The 5-adic expansion of exp(5) is given by A309888.
Approximations of exp(p) in p-adic field: A309900 (p=3), this sequence (p=5), A309904 (p=7).

Programs

  • PARI
    a(n) = lift(exp(5 + O(5^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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