A226109 Triangular numbers t such that t - 4, t - 2, t + 2, t + 4 are four primes.
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
Keywords
Programs
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Java
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); } } }
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Magma
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 -
Mathematica
Select[Accumulate[Range[0, 70]], Union[PrimeQ[{# - 4, # - 2, # + 2, # + 4}]] == {True} &] (* Alonso del Arte, May 27 2013 *)
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