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

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

1,1

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

Links

Charles R Greathouse IV and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 155 terms from Charles R Greathouse IV)

Formula

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

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 *)

Prog

(Magma) [n^2: n in [5..5*10^5] | Set(Intseq(n^2)) subset {2, 3, 5, 7}];  // Bruno Berselli, Jun 06 2011
(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

Crossrefs

Cf. A077676, A030485.

Sequence in context: A058426 A189275 A048384 * A030485 A036509 A034981

Adjacent sequences: A191483 A191484 A191485 * A191487 A191488 A191489

Keyword

nonn,base

Author

Giovanni Teofilatto, Jun 03 2011

Status

approved