A129752 -id:A129752 - cp's OEIS frontend

A171569 Triangular numbers T such that T-2 is a prime.

15, 21, 45, 55, 91, 105, 153, 231, 253, 351, 435, 465, 595, 703, 741, 861, 1035, 1225, 1431, 1485, 1711, 1891, 1953, 2145, 2701, 3003, 3081, 3321, 3741, 4005, 4095, 4465, 4753, 5565, 5671, 6555, 7021, 7875, 8515, 9045, 10011, 10153, 10731, 11175, 11781

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 11 2009

nonn

			15-2 = 13, 21-2 = 19, 45-2 = 43, ...

Cf. A000217, A129545, A129752.

Select[s=0;Table[n*(n+1)/2,{n,6!}],PrimeQ[ #-2]&]
Select[Accumulate[Range[200]],PrimeQ[#-2]&] (* Harvey P. Dale, Apr 09 2018 *)

A171570 Triangular numbers T such that T+2 is a prime.

Original entry on oeis.org

1, 3, 15, 21, 45, 105, 171, 231, 351, 465, 561, 741, 861, 1275, 1431, 1485, 2211, 2415, 2775, 3081, 3321, 4005, 4371, 5151, 7875, 8385, 10731, 11175, 11781, 13041, 13695, 14535, 15051, 15225, 17205, 17391, 17955, 18915, 21321, 22155, 23871, 24531

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 11 2009

nonn

			1+2=3, 3+2=5, 15+2=17, ..

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000217, A129545, A129752, A171569.

Select[s=0;Table[n*(n+1)/2,{n,6!}],PrimeQ[ #+2]&]
Select[Accumulate[Range[300]],PrimeQ[#+2]&] (* Harvey P. Dale, Jun 27 2017 *)

A226109 Triangular numbers t such that t - 4, t - 2, t + 2, t + 4 are four primes.

Original entry on oeis.org

15, 105, 1485, 18915, 666435, 2143485, 4174605, 10059855, 10440165, 28196295, 95295915, 124591005, 155064855, 171023265, 206258205, 298400235, 311737965, 347701635, 389470095, 459332895, 460424685, 498948255, 526517475, 537575655, 615496155, 645500415, 885763005, 963144105

Offset: 1

Alex Ratushnyak, May 26 2013

nonn

Subsequence of A129752.

Proper subsequence of A226196. - Alex Ratushnyak, May 30 2013

Cf. A000217, A024675, A129752, A130178, A226196.

import java.math.BigInteger;
public class A226109 {
    public static void main (String[] args) {
      for (long n = 1; n < (1L << 31); n++) {
          long p2 = n * (n + 1)/2 + 2, m2 = p2 - 4;
          BigInteger b = BigInteger.valueOf(p2);
          if (!b.isProbablePrime(80)) continue;
          b = BigInteger.valueOf(m2);
          if (!b.isProbablePrime(80)) continue;
          b = BigInteger.valueOf(p2 + 2);
          if (!b.isProbablePrime(80)) continue;
          b = BigInteger.valueOf(m2 - 2);
          if (!b.isProbablePrime(80)) continue;
          System.out.printf("%d, ", p2 - 2);
      }
    }
}

A000217:=func; [A000217(t): t in [0..10^5] | forall{A000217(t)+i: i in [-4,-2,2,4] | IsPrime(A000217(t)+i)}]; // Bruno Berselli, May 27 2013

Select[Accumulate[Range[0, 70]], Union[PrimeQ[{# - 4, # - 2, # + 2, # + 4}]] == {True} &] (* Alonso del Arte, May 27 2013 *)

cp's OEIS Frontend

A171569 Triangular numbers T such that T-2 is a prime.

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A171570 Triangular numbers T such that T+2 is a prime.

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Mathematica

A226109 Triangular numbers t such that t - 4, t - 2, t + 2, t + 4 are four primes.

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