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.

A061230 Numbers k such that k + the reversal of k is a square.

Original entry on oeis.org

0, 2, 8, 29, 38, 47, 56, 65, 74, 83, 92, 110, 143, 164, 198, 242, 263, 297, 341, 362, 396, 440, 461, 495, 560, 594, 693, 792, 891, 990, 10100, 10148, 10340, 10395, 10403, 10683, 10908, 10980, 11138, 11330, 11385, 11673, 11970, 12128, 12320, 12375
Offset: 1

Views

Author

Amarnath Murthy, Apr 23 2001

Keywords

Examples

			8 is a term as 8 + 8 = 16 = 4^2.
56 is a term as 56 + 65 = 121 = 11^2.

Links

Crossrefs

Cf. A056964, A061231.
Cf. A359011 (for squares).

Programs

  • Maple
    digrev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
select(t -> issqr(t+digrev(t)),[$0..20000]); # Robert Israel, May 04 2015
  • Mathematica
    Select[Range[0,15000],IntegerQ[Sqrt[#+FromDigits[Reverse[ IntegerDigits[#]]]]]&]  (* Harvey P. Dale, Apr 18 2011 *)
  • PARI
    isok(n) = issquare(n + fromdigits(Vecrev(digits(n)))); \\ Michel Marcus, Aug 04 2019
  • Python
    from math import isqrt
def issquare(n): return isqrt(n)**2 == n
def ok(n): return issquare(n + int(str(n)[::-1]))
print([k for k in range(12376) if ok(k)]) # Michael S. Branicky, Dec 09 2022

Extensions

Corrected and extended by Patrick De Geest, May 28 2001
Edited by N. J. A. Sloane, Jul 24 2009

A227371 Numbers n such that prime(n) + reversal(prime(n)) is a square.

Original entry on oeis.org

1, 10, 15, 23, 56, 89, 2279, 2581, 2683, 6329, 7845, 7942, 26074, 26146, 26290, 26651, 26871, 27080, 27960, 28687, 28898, 29396, 29539, 29824, 30038, 30333, 30404, 30472, 30955, 31025, 31097, 31168, 32076, 32143, 32429, 33502, 33564, 41608, 42011, 42148, 42696
Offset: 1

Views

Author

K. D. Bajpai, Jul 08 2013

Keywords

Comments

See A059799 for the sequence of prime numbers.

Examples

			a(2)=10: prime(10)=29. Reversing digits gives 92. 29+92 = 121 = 11^2.

Links

Crossrefs

Cf. A061231.

Programs

  • Maple
    with(StringTools):
K := proc(n) local a,b,d,e; a :=ithprime(n): b:=parse(Reverse(convert((a),string))): d:=a+b;e:=evalf(sqrt(d));if e=floor(e) then RETURN (n) fi:
end:
seq(K(n), n=1..100000); # K. D. Bajpai, Jul 08 2013
with(StringTools):
K:=proc()local n,a,b,c,d,e; c:=1; for n from 1 to 2000000 do; a:=ithprime(n);b:=parse(Reverse(convert((a),string)));d:=a+b;e:=evalf(sqrt(d));if e=floor(e) then lprint(c,n);c:=c+1;fi;od; end: K(); # K. D. Bajpai, Jul 08 2013
  • Mathematica
    Select[Range[50000],IntegerQ[Sqrt[Prime[#]+IntegerReverse[Prime[#]]]]&] (* The program uses the IntegerReverse function from Mathematica version 10 *) (* Harvey P. Dale, Jan 24 2016 *)

A289140 Positive numbers k such that rev(k)^2 + rev(k^2) is a square, where rev(n) = A004086(n) is the digital reverse of n.

Original entry on oeis.org

998586, 3632658, 9985860, 36326580, 74471091, 99664458, 99858600, 363265800, 634826115, 743193501, 744710910, 756335085, 759317343, 996644580, 998586000, 3632658000, 6348261150, 7177621788, 7431935010, 7447109100, 7563350850, 7593173430, 9966445800
Offset: 1

Views

Author

Giovanni Resta, Jun 26 2017

Keywords

Comments

Every term must be a multiple of 3.

Examples

			998586 is a term since rev(998586^2) + 685899^2 = 1079100^2.

Crossrefs

Cf. A004086, A061230, A061231, A068536, A102859, A113798, A202386, A256515.

Programs

  • Mathematica
    rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; Parallelize@ Select[3 Range[4 10^6], IntegerQ@ Sqrt[rev[#^2] + rev[#]^2] &]
  • PARI
    isok(n) = issquare(fromdigits(Vecrev(digits(n)))^2 + fromdigits(Vecrev(digits(n^2)))); \\ Michel Marcus, Jun 29 2017
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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