OFFSET
1,1
COMMENTS
p*(p + 1)/2 is the first number in a set of three triangular numbers with prime indices in arithmetic progression with difference 420*p*(p + 1) + 105. - Arkadiusz Wesolowski, Oct 29 2013
REFERENCES
Wacław Sierpiński, 200 zadan z elementarnej teorii liczb, Warsaw: PZWS, 1964, pp. 12, 61.
Wacław Sierpiński, 250 Problems in Elementary Number Theory. (Modern Analytic and Computational Methods in Science and Mathematics, No. 26), American Elsevier Publishing Co., Inc., New York; PWN Polish Scientific Publishers, Warsaw, 1970, pp. 7, 50.
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
MATHEMATICA
lst = {}; Do[p = Prime[n]; If[PrimeQ[29*p + 14] && PrimeQ[41*p + 20], AppendTo[lst, p]], {n, 10^3}]; lst
Select[Prime[Range[1000]], AllTrue[{29#+14, 41#+20}, PrimeQ]&] (* Harvey P. Dale, Oct 05 2022 *)
PROG
(Magma) [p : p in PrimesUpTo(7333) | IsPrime(29*p+14) and IsPrime(41*p+20)]; // Arkadiusz Wesolowski, Oct 29 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Arkadiusz Wesolowski, Jan 13 2012
STATUS
approved