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.

A191486 Squares using only the prime digits (2,3,5,7).

Original entry on oeis.org

25, 225, 7225, 27225, 55225, 235225, 2772225, 3553225, 23377225, 33235225, 57532225, 227557225, 252333225, 277722225, 337273225, 357777225, 523723225, 735223225, 777573225, 2523555225, 3325252225, 3377353225, 5232352225, 7333353225
Offset: 1

Views

Author

Giovanni Teofilatto, Jun 03 2011

Keywords

Comments

a(n) = 225 mod 1000 for n > 1. - Charles R Greathouse IV, May 14 2013
The sequence is infinite: it contains A030485 as an infinite proper subsequence which in turn contains all numbers of the form ((5*10^n-5)/3)^2 as a proper subsequence. - M. F. Hasler, Sep 16 2016

Crossrefs

Programs

  • Magma
    [n^2: n in [5..5*10^5] | Set(Intseq(n^2)) subset {2,3,5,7}];  // Bruno Berselli, Jun 06 2011
    
  • Maple
    for b from 1 do convert(convert(b^2,base,10),set) ; if % minus {2,3,5,7} = {} then printf("%d,\n",b^2) ; end if; end do: # R. J. Mathar, Jun 03 2011
  • Mathematica
    w = Boole@! PrimeQ@ # & /@ RotateLeft@ Range[0, 9]; Select[Range[10^5]^2, Total@ Pick[DigitCount@ #, w, 1] == 0 &] (* Michael De Vlieger, Aug 15 2016 *)
  • PARI
    toprime(n,k)=n<<=2;sum(i=0,k-1,n>>=2;[2,3,5,7][bitand(n,3)+1]*10^i)
    v=List([25]);for(k=0,9,for(n=0,4^k-1,t=1000*toprime(n,k)+225;if(issquare(t),listput(v,t)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, May 14 2013
    
  • Python
    from math import isqrt
    def aupto(limit):
      alst, rootlimit = [], isqrt(limit)
      for k in range(1, rootlimit+1):
        if set(str(k*k)) <= set("2357"): alst.append(k*k)
      return alst
    print(aupto(7333353225)) # Michael S. Branicky, May 15 2021

Formula

a(n) = A275971(n)^2. - M. F. Hasler, Sep 16 2016

A030487 When squared gives number composed of digits {2, 5, 7}.

Original entry on oeis.org

5, 15, 85, 165, 235, 1665, 15085, 16665, 166665, 268835, 1666665, 5076665, 16666665, 52683515, 165898335, 166666665, 278433515, 507668915, 850032485, 1508559835, 1666666665, 15085017485, 16666666665, 166666666665
Offset: 1

Views

Author

Keywords

Examples

			5^2 = 25, so 5 is in the sequence.
15^2 = 225, so 15 is in the sequence.
25^2 = 625, which has a 2 and 5 but also a 6, so 25 is not in the sequence.
		

Crossrefs

Cf. A030485.

Programs

  • Mathematica
    Select[5Range[1, 9999, 2], Complement[IntegerDigits[#^2], {2, 5, 7}] == {} &] (* Alonso del Arte, Feb 25 2020 *)

Extensions

Extended and corrected by author 03/2000.
More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 03 2005

A119166 Triangular numbers composed of digits {2,5,7}.

Original entry on oeis.org

55, 2775, 255255, 577275, 572755525755, 2577527227575, 727275225222727525, 2257227755272522252275, 52722757572552577725225, 272527775757277272275522727772752527575
Offset: 1

Views

Author

Giovanni Resta, May 10 2006

Keywords

Comments

a(11) > 10^40. - Tyler Busby, Mar 28 2023

Crossrefs

Cf. A000217, A030485, A119167. See A119033 for a table of cross-references.

Formula

a(n) = A000217(A119167(n)). - Tyler Busby, Mar 28 2023

Extensions

a(10) from Tyler Busby, Mar 28 2023

A361821 Perfect powers in A329150.

Original entry on oeis.org

25, 27, 32, 225, 2025, 2197, 2500, 3025, 3375, 7225, 11025, 13225, 21952, 22500, 27000, 27225, 55225, 70225, 112225, 133225, 172225, 195112, 202500, 207025, 235225, 250000, 255025, 302500, 319225, 511225, 555025, 570025, 722500, 1102500, 1113025, 1177225, 1311025
Offset: 1

Views

Author

Bernard Schott, Mar 25 2023

Keywords

Comments

No term has a digit 4, 6 or 8.
Subsequences of squares are listed in Crossrefs.

Examples

			32 is a term since A329147(21) = 32 = 2^5.
2197 is a term since A329147(194) = 2197 = 13^3.
235225 is a term since A329147(123113) = 235225 = 485^2.
		

Crossrefs

Intersection of A001597 and A329150.
Cf. A329147.
Subsequences of squares with specified digits: A058426 (0,2,5), A053919 (2,3,5), A030485 (2,5,7), A191486 (2,3,5,7).

Programs

  • Mathematica
    p[n_] := If[n > 0, Prime[n], 0]; ppQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1; seq[ndigmax_] := Module[{t = Table[FromDigits[Flatten@ IntegerDigits@ (p /@ IntegerDigits[n])], {n, 0, 10^ndigmax - 1}]}, Union@ Select[t, 0 < # < 10^ndigmax && ppQ[#] &]]; seq[6] (* Amiram Eldar, Mar 26 2023 *)
  • PARI
    f(n) = if (n, fromdigits(concat(apply(d -> if (d, digits(prime(d)), [0]), digits(n)))), 0); \\ A329147
    lista(nn) = my(list = List(), m); for (n=0, nn, m = f(n); if ((m <= nn) && ispower(m), listput(list, m));); vecsort(Set(list)); \\ Michel Marcus, Mar 26 2023
Showing 1-4 of 4 results.