A265211 - OEIS

%I #14 Sep 08 2022 08:46:14

%S 25,36,196,676,1936,2116,3136,4096,5476,5776,7396,8836,11236,21316,

%T 23716,26896,42436,51076,55696,59536,64516,65536,75076,81796,87616,

%U 92416,98596,106276,118336,119716,132496,179776,190096,198916,206116,215296,256036,274576,287296

%N Squares that become prime when their rightmost digit is removed.

%C All the terms in this sequence, except a(1) end in digit 6.

%C All the terms except a(2) are congruent to 1 (mod 3).

%C All terms except a(1) are of the form 10*p+6 where p is a prime of the form 10*x^2 + 8*x + 1 or 10*x^2 + 12*x + 3. The Bunyakovsky conjecture implies that there are infinitely many of both of these types. - _Robert Israel_, Jan 12 2016

%H K. D. Bajpai, <a href="/A265211/b265211.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bunyakovsky_conjecture">Bunyakovsky conjecture</a>.

%e 196 = 14^2 becomes the prime 19 when its rightmost digit is removed.

%e 3136 = 56^2 becomes the prime 313 when its rightmost digit is removed.

%p select(t -> isprime(floor(t/10)), [seq(i^2, i=1..1000)]); # _Robert Israel_, Jan 12 2016

%t A265211 = {}; Do[k = n^2; If[PrimeQ[Floor[k/10]], AppendTo[A265211 , k]], {n, 1500}]; A265211

%t Select[Range[540]^2,PrimeQ[FromDigits[Most[IntegerDigits[#]]]]&] (* _Harvey P. Dale_, Aug 02 2016 *)

%o (PARI) for(n=1,1000, k=n^2; if(isprime(k\10), print1(k, ", ")));

%o (Magma) [k: n in [1..100] | IsPrime(Floor(k/10)) where k is n^2];

%Y Cf. A000290, A225873, A225885, A226354, A226531.

%K nonn,base,easy

%O 1,1

%A _K. D. Bajpai_, Dec 05 2015