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 1-7 of 7 results.

A074841 Square root of n contains n as a string of digits to the immediate right of the decimal point (excluding leading zeros).

Original entry on oeis.org

8, 77, 5711, 9797, 77327, 997997, 8053139, 60755907, 62996069, 99979997, 9999799997, 71515443427, 76933604839, 93445113269, 999997999997
Offset: 1

Views

Author

Paul Lusch, Sep 09 2002

Keywords

Comments

All numbers of the form (10^n-3)*(10^n+1), n > 0, are members. - Robert G. Wilson v, Aug 02 2004

Examples

			The square root of 77327 = 278.077327...

Links

Crossrefs

Cf. A232086, A232110, A074762.

Programs

  • Mathematica
    f[n_] := Block[{l = Floor[ Log[10, n] + 1], rd = RealDigits[ Sqrt[n], 10, 24], id = IntegerDigits[n]}, rdd = Drop[ rd[[1]], rd[[2]]]; While[ rdd[[1]] == 0, rdd = Drop[rdd, 1]]; Take[rdd, l] == id]; Do[ If[ StringPosition[ ToString[ N[ Sqrt[n], 24]], ToString[n]] != {}, If[ f[n], Print[n]]], {n, 2, 6 10^8}] (* Robert G. Wilson v, Aug 02 2004 *)
  • PARI
    /* Uses PARI functions provided in link
* Sample run uses a = [0,12], b=10, p=2, direct=True */
GetAllGIs(0,12,10,2,1) \\ Robert Tanniru, Nov 20 2013

Extensions

More terms from Robert G. Wilson v, Aug 02 2004
New term a(13) inserted by Robert Tanniru, Nov 20 2013

A232086 Third root of n contains n as a string of digits to the immediate right of the decimal point (excluding leading zeros).

Original entry on oeis.org

2, 39, 48570, 70293094, 97959170, 383263523, 7141269931, 52167799575, 54592884236, 80834974860, 3224757993012, 8391216236921, 174753523862043, 2248771925089484, 355191775894066192, 758148263300700696, 3004862096444523247, 9336508574693449683, 71580261944407825851
Offset: 1

Views

Author

Robert Tanniru, Nov 17 2013

Keywords

Examples

			97959170^(1/3) = 460.97959170151...

Links

Crossrefs

Cf. A074841, A232110, A074762

Programs

  • PARI
    /* PARI functions provided in extra link. */
/* Sample Run Using a = [0,12], b=10, p=3 */
GetAllGIs(0,12,10,3,1)

Extensions

a(11)-a(12) added by Robert Tanniru, Nov 20 2013
More terms from Bert Dobbelaere, Jun 23 2024

A232110 Fourth root of n contains n as a string of digits to the immediate right of the decimal point (excluding leading zeros).

Original entry on oeis.org

3, 4, 27, 1913227, 9821998, 3588613885932, 7625632704605, 50859949338383, 21029300554772499, 97202454420912990, 440023525444970228, 783944985766933369, 1277151495727998611, 2283977463662240937, 72927208535053310211, 365439872472838714161, 740751647624914930138
Offset: 1

Views

Author

Robert Tanniru, Nov 18 2013

Keywords

Examples

			1913227^(1/4) = 37.19132279207...

Links

Crossrefs

Cf. A074841, A232086, A074762.

Programs

  • PARI
    isok(n) = {if (ispower(n, 4), return (0)); fr = frac(n^(1/4)); while (frac(fr) < 1/10, fr *= 10); nd = length(digits(n)); fr *= 10^nd; floor(fr) == n;} \\ Michel Marcus, Nov 20 2013
  • PARI
    /*Sample Run Using a = [0,14], b=10, p=4 using PARI code in link */
GetAllGIs(0,14,10,4,1)

Extensions

More terms from Bert Dobbelaere, Jun 23 2024

A074119 Seventh root of n contains n as a string of digits to the immediate right of the decimal point (excluding leading zeros).

Original entry on oeis.org

89, 90, 16874, 25077, 479505, 306577056, 3821075079, 18014062431, 23075041700, 7240367851167, 85944742335578, 359069276640550, 809162747122740, 41275883437937369, 3209114244021563000, 69831531751710887320, 236842309259501676015, 12355587970480207660102, 79903263070494746587634
Offset: 1

Views

Author

Paul Lusch, Sep 16 2002

Keywords

Examples

			Seventh root of 16874 = 4.016874...

Links

Crossrefs

Cf. A074762, A074841.

Extensions

More terms from Bert Dobbelaere, Jun 23 2024

A096257 The least k whose n-th root contains k as a string of digits to the immediate right of the decimal point (excluding leading zeros).

Original entry on oeis.org

8, 2, 3, 633, 19703, 89, 69, 56, 46, 39, 33, 29, 25, 22, 20, 18, 16, 14, 13, 12, 11, 10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 138, 133, 128, 124, 120, 116, 113, 109, 106, 103, 100, 97, 95, 92, 90, 87, 85, 83, 81, 79, 77, 75, 74, 72, 70, 69, 67, 66, 65, 63, 62, 61, 59, 58, 57
Offset: 2

Views

Author

Paul Lusch and Robert G. Wilson v, Jul 31 2004

Keywords

Crossrefs

Cf. A074841, A074762.

Programs

  • Mathematica
    f[k_, n_] := Block[{l = Floor[ Log[10, k] + 1], rd = RealDigits[ k^(1/n), 10, 24], id = IntegerDigits[k]}, rdd = Drop[ rd[[1]], rd[[2]]]; While[ rdd[[1]] == 0, rdd = Drop[rdd, 1]]; Take[rdd, l] == id]; g[n_] := Block[{k = 2}, While[IntegerQ[k^(1/n)] || f[k, n] == False, k++ ]; k]; Table[ g[n], {n, 2, 72}]
  • Python
    import re
from sympy import perfect_power
from decimal import *
getcontext().prec = 24
def lzs(s): return len(s) - 2 - len(s[2:].lstrip('0')) # # of leading zeros
def cond(sk, sroot, k, n): # is condition true, with precision verification
    if perfect_power(k, [n]): return False # decimal part should be all 0's
    assert lzs(sroot) + len(sk) < len(sroot) - 3, (n, "increase precision")
    return re.match("0.0*"+sk, sroot)
def a(n):
    k, power = 1, Decimal(1)/Decimal(n)
    rootk, sk = Decimal(k)**power, str(k)
    while not cond(sk, str(rootk - int(rootk)), k, n):
        k += 1
        rootk, sk = Decimal(k)**power, str(k)
    return k
print([a(n) for n in range(2, 73)]) # Michael S. Branicky, Aug 02 2021

A099400 Square root of a(n) contains the n-th prime as a string of digits to the immediate right of the decimal point (excluding leading zeros).

Original entry on oeis.org

5, 11, 21, 3, 83, 124, 201, 27, 5, 28, 11, 179, 2, 89, 20, 91, 92, 58, 114, 50, 3, 23, 34, 24, 288, 2411, 581, 1377, 1031, 489, 1531, 366, 849, 632, 406, 536, 367, 2721, 13495, 537, 634, 492, 686, 331, 1866, 408, 52, 409, 485, 688, 297, 742, 1105, 12377, 856, 1174
Offset: 1

Views

Author

Gil Broussard, Nov 17 2004

Keywords

Examples

			a(1)= 5 because sqrt( 5)=2.(2)236...
a(2)=11 because sqrt(11)=3.(3)316...
a(3)=21 because sqrt(21)=4.(5)825...
a(4)= 3 because sqrt( 3)=1.(7)320...
...
a(100) =1125 because sqrt(1125)=33.5410... and 541 is the 100th prime.

Crossrefs

Cf. A074841, A074762.

A099401 Square root of a(n) contains the n-th Fibonacci number as a string of digits to the immediate right of the decimal point (excluding leading zeros).

Original entry on oeis.org

10, 10, 5, 11, 21, 8, 124, 52, 54, 43, 24, 970, 297, 457, 467, 1520, 2516, 7269, 12414, 3804, 11048, 25020, 135635, 56389, 710228, 44151, 21082, 762684, 696414, 1085414, 6472621, 2979828, 15220551, 72130, 9934617, 79533387
Offset: 1

Views

Author

Gil Broussard, Nov 17 2004

Keywords

Examples

			a(1)= 10 because sqrt( 10)= 3.(1)622...
a(2)= 10 because sqrt( 10)= 3.(1)622...
a(3)= 5 because sqrt( 5)= 2.(2)360...
a(4)= 11 because sqrt( 11)= 3.(3)166...
a(5)= 21 because sqrt( 21)= 4.(5)825...
a(6)= 8 because sqrt( 8)= 2.(8)284...
a(7)= 124 because sqrt(124)=11.(13)55...
etc.

Crossrefs

Cf. A074841, A074762.

Programs

  • Mathematica
    Do[x = IntegerDigits[Fibonacci[n]]; i = 1; l = {}; While[l != x, d = RealDigits[N[Sqrt[i], 100]]; l = Take[Drop[First[d], Last[d]], Length[x]]; i++ ]; Print[i-1], {n, 1, 36}] (* Ryan Propper, Aug 11 2005 *)

Extensions

Corrected and extended by Ryan Propper, Aug 11 2005
Showing 1-7 of 7 results.

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