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.

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A043347 To form the sequence, write the primes 2, 3, 5, 7,... as an infinite string 2357111317...; then take the first 2 digits of the string, 23, then the next 3 digits, 571, then the next 5 digits, 11317, then the next 7 digits, 1923293, then... (stepping through prime numbers of digits). Omit any leading 0's.

Original entry on oeis.org

23, 571, 11317, 1923293, 13741434753, 5961677173798, 38997101103107109, 1131271311371391491, 51157163167173179181191, 19319719921122322722923323924, 1251257263269271277281283293307
Offset: 1

Views

Author

Joseph L. Pe, Jan 12 2002

Keywords

Crossrefs

The first four terms of the sequence are primes - see A066776.

Programs

  • Mathematica
    a[n_] := (k = Prime[ Floor[n^(3/2)]] + 6; l = Sum[ Prime[i], {i, 1, n - 1} ]; b = ""; Do[ b = StringJoin[b, ToString[ Prime[i]]], {i, 1, k} ]; Return[ ToExpression[ StringTake[ StringDrop[b, l], Prime[n]]]]); Table[ a[n], {n, 1, 13} ]

Extensions

More terms from Robert G. Wilson v, Jan 16 2002

A139031 Imaginary part of (4 + 3i)^n.

Original entry on oeis.org

3, 24, 117, 336, -237, -10296, -76443, -354144, -922077, 1476984, 34867797, 242017776, 1064447283, 2465133864, -6890111163, -116749235904, -761741108157, -3175197967656, -6358056037323, 28515500892816, 387075408075603, 2383715742284424, 9392840736385317, 15549832333971936
Offset: 1

Views

Author

Gary W. Adamson, Apr 06 2008

Keywords

Comments

Division of each term by 3 generates an integer sequence 1, 8, 39, 112, -79, -3432, -25481, -118048, -307359, 492328, ... - R. J. Mathar, Apr 08 2008

Examples

			a(3) = 117 since (4 + 3i)^3 = (-44 + 117i).
a(4) = 336 = 8*a(3) - 25*a(2) = 8*117 - 25*24.
a(3) = 117 = term (2,1) of [4,-3; 3,4]^3.

Links

Crossrefs

Cf. A139030, A066771, A066776.

Programs

Formula

Imaginary part of (4 + 3i)^n.
Term (2,1) of [4,-3; 3,4]^n.
a(n)^2 + A139030(n)^2 = 5^(2*n).
a(n) = 8*a(n-1) - 25*a(n-2), n>2, given a(1) = 3, a(2) = 24.
(unsigned): Odd-indexed terms of A066771 interleaved with even-indexed terms of A066776.
O.g.f.: 3*x/(1-8*x+25*x^2). - R. J. Mathar, Apr 08 2008
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