A226354 -id:A226354 - cp's OEIS frontend

A226531 Cubes that become prime when their least-significant (rightmost) digit is removed.

27, 3375, 4096, 4913, 35937, 97336, 110592, 148877, 421875, 681472, 1191016, 1442897, 1560896, 2628072, 3241792, 3581577, 3869893, 4741632, 5359375, 8998912, 10218313, 12649337, 16777216, 16974593, 21253933, 26730899, 31255875, 32157432, 43986977, 45882712

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, Jun 09 2013

			4096 = 16^3, and becomes the prime number 409 when truncated.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Cf. A226090.

Cf. A024770, A225873, A225885, A226354.

Select[Range[1000]^3,PrimeQ[Floor[#/10]]&] (* Harvey P. Dale, May 28 2021 *)

library(gmp)trimR=function(x) { x=as.character(x); ifelse(nchar(x)<2,0,substr(x,1,nchar(x)-1)) }
y=as.bigz(rep(0,10000)); len=0; n=as.bigz(-1)
while(len<10000) if(isprime(trimR((n=n+1)^3))) y[(len=len+1)]=n^3

A234787 Cubes (with at least two digits) that become squares when their rightmost digit is removed.

Original entry on oeis.org

1000, 64000, 729000, 4096000, 15625000, 46656000, 117649000, 262144000, 531441000, 1000000000, 1771561000, 2985984000, 4826809000, 7529536000, 11390625000, 16777216000, 24137569000, 34012224000, 47045881000, 64000000000

Offset: 1

Reiner Moewald, Dec 30 2013

With the help of the Nagell-Lutz theorem it is easy to prove that there are no other solutions than those of the form 1000*n^6.

Georg Fischer, Table of n, a(n) for n = 1..300 [a(1..204) from Reiner Moewald]
Wikipedia, Nagell-Lutz theorem.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A226354.

Subsequence of A000578.

lista(nn) = {for (n=1, nn, if (((cb = n^3) > 10) && issquare(cb\10), print1(cb, ", ")););} \\ Michel Marcus, Jan 10 2014

Vec(1000*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Dec 15 2019

a(n) = 1000*n^6.
From Colin Barker, Dec 15 2019: (Start)
G.f.: 1000*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

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

Original entry on oeis.org

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

K. D. Bajpai, Dec 05 2015

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

			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.

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

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

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

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

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 *)

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

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A226531 Cubes that become prime when their least-significant (rightmost) digit is removed.

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A234787 Cubes (with at least two digits) that become squares when their rightmost digit is removed.

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

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