A265211 Squares that become prime when their rightmost digit is removed.

25, 36, 196, 676, 1936, 2116, 3136, 4096, 5476, 5776, 7396, 8836, 11236, 21316, 23716, 26896, 42436, 51076, 55696, 59536, 64516, 65536, 75076, 81796, 87616, 92416, 98596, 106276, 118336, 119716, 132496, 179776, 190096, 198916, 206116, 215296, 256036, 274576, 287296

Offset

1,1

Comments

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

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

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

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Wikipedia, Bunyakovsky conjecture.

Example

196 = 14^2 becomes the prime 19 when its rightmost digit is removed.
3136 = 56^2 becomes the prime 313 when its rightmost digit is removed.

Maple

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

Mathematica

A265211 = {}; Do[k = n^2; If[PrimeQ[Floor[k/10]], AppendTo[A265211 , k]], {n, 1500}]; A265211
Select[Range[540]^2, PrimeQ[FromDigits[Most[IntegerDigits[#]]]]&] (* Harvey P. Dale, Aug 02 2016 *)

Prog

(PARI) for(n=1, 1000, k=n^2; if(isprime(k\10), print1(k, ", ")));
(Magma) [k: n in [1..100] | IsPrime(Floor(k/10)) where k is n^2];

Crossrefs

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

Sequence in context: A029781 A161783 A066217 * A205644 A077437 A077676

Adjacent sequences: A265208 A265209 A265210 * A265212 A265213 A265214

Keyword

nonn,base,easy

Author

K. D. Bajpai, Dec 05 2015

Status

approved