Pablo Martínez - cp's OEIS frontend

User: Pablo Martínez

Pablo Martínez has authored 2 sequences.

A210205 The sum of three consecutive prime numbers, beginning with a(n), is a cube.

439, 34603, 1016201, 3696493, 4002991, 6344687, 10221397, 14662309, 16209029, 19925483, 20856907, 22805969, 43441271, 60120691, 60761413, 62056457, 62710787, 87791567, 96268243, 125977651, 166225747, 170027449

Offset: 1

Pablo Martínez, Mar 18 2012

nonn

			prime(85) + prime(86) + prime(87) = 439 + 443 + 449 = 1331 = 11^3.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A061308.

t = {}; p = 2; q = 3; Do[r = NextPrime[q]; If[IntegerQ[(p + q + r)^(1/3)], AppendTo[t, p]; Print[p]]; p = q; q = r, {1000000}]; t (* T. D. Noe, Mar 24 2012 *)
Select[Partition[Prime[Range[9505000]],3,1],IntegerQ[Surd[Total[#],3]]&][[All,1]] (* Harvey P. Dale, May 22 2020 *)

from _future_ import division
from sympy import nextprime, prevprime
A210205_list = []
for i in range(3,10**6):
    n = i**3
    p2 = prevprime(n//3)
    p1, p3 = prevprime(p2), nextprime(p2)
    q = p1+p2+p3
    while q <= n:
        if q == n:
            A210205_list.append(p1)
        p1, p2, p3 = p2, p3, nextprime(p3)
        q = p1+p2+p3 # Chai Wah Wu, Dec 31 2015

Extended by T. D. Noe, Mar 24 2012

A198863 Numbers whose squares are pandigital numbers with exactly two occurrences of each digit.

Original entry on oeis.org

3164252736, 3164326683, 3164389113, 3164391957, 3164406057, 3164416923, 3164421333, 3164454864, 3164466768, 3164482974, 3164528124, 3164547114, 3164689392, 3164695206, 3164735277, 3164770866, 3164789766, 3164863185, 3164867118, 3164907357, 3165009693

Offset: 1

Pablo Martínez, Oct 30 2011

Later terms include: 4000171725, 4000183233, 4000198443, 4000203567.

Because the sum of the digits of a(n)^2 is 90, 9 divides a(n)^2. Hence, 3 divides a(n). - T. D. Noe, Nov 08 2011

			4000171725^2 = 16001373829489475625.

Cf. A156977 (n^2 contains each digit once).

Select[Range[3164250000, 3164450000], Union[DigitCount[#^2]] == {2} &] (* Alonso del Arte, Oct 31 2011 *)
t = {}; n = 3164211348; nMax = 9994386752; While[n <= nMax && Length[t] < 21, While[n <= nMax && Union[DigitCount[n^2]] != {2}, n = n + 3]; If[n <= nMax, AppendTo[t, n]; Print[n]; n = n + 3]]; t (* T. D. Noe, Nov 08 2011 *)

All displayed terms are from Charles R Greathouse IV, Alonso del Arte and T. D. Noe, Nov 08 2011

cp's OEIS Frontend

User: Pablo Martínez

A210205 The sum of three consecutive prime numbers, beginning with a(n), is a cube.

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