A161853 Primes which are anagrams of squares.

61, 163, 211, 487, 613, 619, 631, 691, 829, 1237, 1279, 1297, 1327, 1483, 1489, 1621, 1693, 1723, 1861, 2029, 2053, 2089, 2137, 2161, 2179, 2251, 2371, 2467, 2503, 2521, 2539, 2593, 2647, 2713, 2719, 2731, 2791, 2917, 2953, 2971, 3163, 3169, 3217, 3259

Offset

1,1

Comments

211 is in the sequence because it is a prime number and 121 (an anagram of 211) is a square: 11*11.

829 is in the sequence because it is a prime number and 289 (an anagram of 829) is a square: 17*17.

409 is NOT in the sequence because, although it is a prime and 49 is a square, 49 is not an anagram of 409 because it does not contain the digit zero. In other words, an anagram of a prime, for purposes of this sequence, must have the same number of digits as the prime has. - Harvey P. Dale, Aug 29 2017

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10923 (all terms with <= 6 digits; terms 1..1000 from Harvey P. Dale)

Mathematica

pasQ[n_]:=AnyTrue[Sqrt[#]&/@Select[FromDigits/@Permutations[ IntegerDigits[ n]], IntegerLength[#]==IntegerLength[n]&], IntegerQ]; Select[Prime[ Range[ 500]], pasQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 29 2017 *)

Prog

(Python)
from sympy import primerange
from itertools import count, takewhile
def hash(n): return "".join(sorted(str(n)))
def aupto_digits(d):
    squares = takewhile(lambda x:x<10**d, (i*i for i in count(1)))
    primes  = primerange(1, 10**d)
    S = set(map(hash, squares))
    return [p for p in primes if hash(p) in S]
print(aupto_digits(4)) # Michael S. Branicky, Feb 18 2024

Crossrefs

Sequence in context: A044393 A044774 A138627 * A106096 A142482 A007488

Adjacent sequences: A161850 A161851 A161852 * A161854 A161855 A161856

Keyword

nonn,base

Author

Claudio Meller, Jun 20 2009

Status

approved