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 1-4 of 4 results.

A135605 Consider the infinite string S = 12345678910111213141516171819202122232425262728293031... Sequence gives the first prime that starts at the k-th digit, skipping zero digits.

Original entry on oeis.org

1234567891, 2, 3, 4567, 5, 67, 7, 89, 9101112131, 101, 11, 11, 1213, 2, 13, 3, 14151617, 41, 151, 5, 16171819202122232425262728293031323334353637383940414243, 61, 17, 7, 181, 81920212223242526272829303, 19, 920212223242526272829303132333435363738394041424344454647484950515253
Offset: 1

Views

Author

Marcelo Iglesias (markelo(AT)gmail.com), Feb 26 2008

Keywords

Comments

a(67)>10^5000. - Robert G. Wilson v, Mar 01 2008

Examples

			Examples from _N. J. A. Sloane_, Feb 24 2021: (Start)
S = 1234567891011121314151617181920212...
The 10th digit is a 1, and the first prime in S that starts with that digit is 101.
The 11th digit is 0, so we skip it.
The 12th digit is 1, and the first prime in S that starts with that digit is 11.
The 13th digit is another 1, and the first prime in S that starts with that digit is another 11.
The 14th digit is another 1, and the first prime in S that starts with that digit is 1213.
And so on. (End)

Links

Crossrefs

Cf. A007376, A033307, A073175, A073175, A103575.

Programs

  • Mathematica
    a[n_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = 9 i*10^(i - 1) + l; i++ ]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + 10^(i - 1); If[p != 0, IntegerDigits[q][[p]], Mod[q - 1, 10]]]; pp[j_, k_] := FromDigits[ Table[ a@i, {i, j, k}]]; f[n_] := Block[{m = n, p}, If[a@n != 0, (While[p = pp[n, m]; ! PrimeQ@ p, m++ ]; p),]]; Array[f, 29] (* Robert G. Wilson v, Mar 01 2008 *)

Extensions

More terms from Robert G. Wilson v, Mar 01 2008

A162324 Write the natural numbers as an infinite sequence of digits; starting at the left, cut into the smallest pieces so that each piece is a prime. Leading zeros are thrown away.

Original entry on oeis.org

1234567891, 11, 1213, 14151617, 181, 920212223242526272829303132333435363738394041424344454647484950515253, 5
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 01 2009

Keywords

Comments

This is a "lossy" base-ten sequential-smallest-prime percolation of a Champernowne-substrate. The "lossless" version is A103575. The substrate percolates into identical terms 4-115 for both lossy and lossless versions. Terms 119-155 and 158-221 of the lossy version correspond to terms 117-153 and 155-218, respectively, of the lossless version. No other correspondences are known because of the subsequent interjection of very large primes. (For the purposes of this analysis, large probable primes have been treated as actual primes.)

Examples

			After 1234567891 the next digit is 0 that has to be rejected. Next digits are 11 (prime); then 12, 13 (1213 prime); etc.

Links

Crossrefs

A073175, A103575, A135605

Extensions

Edited by Hans Havermann, Dec 07 2009

A105314 Write the natural numbers as an infinite sequence of digits, starting at the left; a(n) is the subset (i.e., the position in this sequence of the "counting digits") of the first digit of the n-th square.

Original entry on oeis.org

1, 4, 9, 22, 40, 62, 88, 118, 152, 190, 253, 322, 397, 478, 565, 658, 757, 862, 973, 1090, 1213, 1342, 1477, 1618, 1765, 1918, 2077, 2242, 2413, 2590, 2773, 2986, 3246, 3514, 3790, 4074, 4366, 4666, 4974, 5290, 5614, 5946, 6286, 6634, 6990, 7354, 7726, 8106
Offset: 1

Views

Author

Alexandre Wajnberg, Apr 25 2005

Keywords

Examples

			integers  : 1234567891011121314151617...
1st digit : x  x    x            x
positions : 1  4    9           22

Crossrefs

Cf. A103575.

Programs

  • PARI
    a(n) = 1+ sum(k=1, n^2-1, #digits(k)); \\ Michel Marcus, Jul 27 2017

Extensions

More terms from Joshua Zucker, Jun 21 2006

A105930 Starting position of the n-th prime in the almost-natural numbers sequence A007376.

Original entry on oeis.org

2, 3, 5, 7, 12, 16, 24, 28, 36, 48, 52, 64, 72, 76, 84, 96, 108, 112, 124, 132, 136, 148, 156, 168, 184, 193, 199, 211, 217, 229, 271, 283, 301, 307, 337, 343, 361, 379, 391, 409, 427, 433, 463, 469, 481, 487, 523, 559, 571, 577, 589, 607, 613, 643, 661, 679
Offset: 2

Views

Author

Alexandre Wajnberg, Apr 26 2005

Keywords

Comments

Prime number positions in the "counting digits": write the natural numbers as an infinite sequence of digits, starting at the left. a(n) is the subscript (i.e. the position in this sequence of "counting digits") of the first digit of the n-th prime.

Examples

			a(6)=16 because the sixth prime (13) appears at the 16th (and 17th) position in the "counting digits": 123456789101112-13-141516

Crossrefs

Cf. A007376, A103575.

Programs

  • Mathematica
    f[n_] := Block[{d = Floor[ Log[10, n] + 1]}, d(n - 1) - Sum[9i*10^(d - i - 1), {i, d - 1}] + 1]; Table[ f[ Prime[n]], {n, 56}] (* Robert G. Wilson v, Apr 30 2005 *)

Extensions

Edited by Robert G. Wilson v, Apr 30 2005
Showing 1-4 of 4 results.

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