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
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[n^2: n in [5..5*10^5] | Set(Intseq(n^2)) subset {2,3,5,7}]; // Bruno Berselli, Jun 06 2011
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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
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w = Boole@! PrimeQ@ # & /@ RotateLeft@ Range[0, 9]; Select[Range[10^5]^2, Total@ Pick[DigitCount@ #, w, 1] == 0 &] (* Michael De Vlieger, Aug 15 2016 *)
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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
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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
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
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.
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Select[5Range[1, 9999, 2], Complement[IntegerDigits[#^2], {2, 5, 7}] == {} &] (* Alonso del Arte, Feb 25 2020 *)
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
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
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.
Subsequences of squares with specified digits:
A058426 (0,2,5),
A053919 (2,3,5),
A030485 (2,5,7),
A191486 (2,3,5,7).
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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 *)
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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
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