A357474 - OEIS

%I #20 Nov 19 2022 03:28:30

%S 1,4,9,11,14,16,19,25,36,41,44,49,64,81,91,94,99,100,111,114,116,119,

%T 121,125,136,141,144,149,161,164,169,181,191,194,196,199,225,251,254,

%U 256,259,289,324,361,364,369,400,411,414,416,419,425,436,441,444,449,464

%N Squarely correct numbers.

%C A positive integer is a squarely correct number if its base-10 representation consists entirely of one or more adjacent blocks of digits that are positive perfect squares with no leading zeros. (See George Berzsenyi link below.)

%H George Berzsenyi, <a href="https://doi.org/10.1080/10724117.2022.2092341">Consecutively and Squarely Correct (P439)</a>, Math Horizons, Vol. 30, Issue 1, The Playground, August 2022.

%F 5n/3 < a(n) << n^k for n > 1, where k = log 10/log 3 = 2.0959.... - _Charles R Greathouse IV_, Oct 03 2022

%e 14401 is not a term, but 14411 is.

%o (Python)

%o from sympy.ntheory.primetest import is_square

%o def ok(n):

%o     if is_square(n): return True

%o     s = str(n)

%o     return any(s[i]!="0" and ok(int(s[:i])) and ok(int(s[i:])) for i in range(1, len(s)))

%o print([k for k in range(1, 465) if ok(k)]) # _Michael S. Branicky_, Oct 03 2022

%o (PARI) is(n)=if(n<11, issquare(n), n%10, my(d=digits(n)); for(i=1,#d, if(issquare(n%10^i) && d[#d+1-i] && is(n\10^i), return(1))); 0, my(k=valuation(n,10)); k%2==0 && is(n/10^k)) \\ _Charles R Greathouse IV_, Oct 04 2022

%Y Cf. A000290, A036435, A018851.

%K nonn,easy,base

%O 1,2

%A _Freddy Barrera_, Sep 29 2022