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.

A030667 Square root of A030666(n).

Original entry on oeis.org

4, 5, 6, 7, 23, 8, 27, 9, 30, 10, 34, 11, 37, 12, 39, 13, 42, 43, 14, 45, 46, 15, 48, 49, 16, 51, 52, 17, 54, 55, 56, 18, 58, 59, 188, 19, 61, 62, 63, 20, 203, 65, 66, 21, 213, 68, 69, 22, 70, 71, 72, 23, 73, 74, 235, 75, 24, 241, 77, 78, 247, 25, 251, 80, 81
Offset: 1

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Keywords

Crossrefs

Cf. A030666.

A030686 Smallest nontrivial extension of n^2 which is a square.

Original entry on oeis.org

16, 49, 900, 169, 256, 361, 4900, 6400, 8100, 10000, 12100, 1444, 16900, 19600, 22500, 25600, 28900, 3249, 36100, 40000, 44100, 48400, 52900, 57600, 62500, 67600, 72900, 78400, 84100, 90000, 96100, 102400, 108900, 115600, 122500
Offset: 1

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Keywords

Comments

Nontrivial extension means appending at least one digit even if the number is already a square.

Crossrefs

See also A023110 = A031149^2 and A202303 = A031150^2 for a related concept, and cross-references there (and in links) for the analog in bases other than 10. - M. F. Hasler, Sep 28 2014

Formula

a(n) = A030687(n)^2. - M. F. Hasler, Sep 28 2014
a(n) = A030666(n^2). - Alonso del Arte, Apr 01 2020

A030671 Smallest extension of n-th prime which is a square.

Original entry on oeis.org

25, 36, 529, 729, 1156, 1369, 1764, 196, 2304, 2916, 3136, 3721, 41209, 4356, 4761, 5329, 5929, 61009, 676, 71289, 7396, 7921, 83521, 89401, 97344, 101124, 103041, 107584, 109561, 113569, 12769, 131044, 137641, 13924, 149769, 15129
Offset: 1

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Examples

			For n=2, the second prime is 3, and 36 is the smallest square that begins with 3, so a(2) = 36. - _Michael B. Porter_, Sep 06 2016
		

Crossrefs

Programs

  • Maple
    A030666:= proc(x) local d;
    for d from 1 do
      if ceil(sqrt(10^d*x)) <=  floor(sqrt(10^d*(x+1)-1)) then
         return ceil(sqrt(10^d*x))^2
    fi
    od
    end proc:
    seq(A030666(ithprime(i)),i=1..100); # Robert Israel, Sep 05 2016

Formula

a(n) = A030666(A000040(n)). - Robert Israel, Sep 05 2016

Extensions

Name edited by Robert Israel, Sep 06 2016

A264604 a(n) = smallest square which is a concatenation of n and m, where m is a decimal number.

Original entry on oeis.org

16, 25, 36, 49, 529, 64, 729, 81, 961, 100, 1156, 121, 1369, 144, 1521, 169, 1764, 1849, 196, 2025, 2116, 225, 23104, 24336, 256, 26244, 27225, 289, 2916, 3025, 3136, 324, 3364, 3481, 35344, 361, 3721, 3844, 3969, 400, 41209, 4225, 4356, 441, 45369, 4624, 4761, 484, 49284, 5041, 5184, 529, 5329, 5476
Offset: 1

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Author

N. J. A. Sloane, Nov 24 2015

Keywords

Comments

m can be 0 but not 00, so a(9) = 961, in contrast to A030666(9) = 900.

Crossrefs

Similar to A030666 but with a more stringent rule.

Programs

  • Maple
    # Computes 10000 terms
    for b from 1 to 10000 do
    sw1:=-1;
    for n from 0 to 1000000 do
    len:=length(n);
    if len=0 then len:=1; fi;
    t2:=10^len*b+n;
    if issqr(t2) then sw1:=1; lprint(b,t2); break; fi; od:
    if sw1 < 0 then lprint("failed at",b); lprint(b,-1);  fi;
    od:
Showing 1-4 of 4 results.