A203263 Primes p such that 29*p + 14 and 41*p + 20 are also prime.

61, 103, 127, 271, 313, 331, 373, 457, 547, 571, 577, 613, 877, 967, 997, 1201, 1423, 1597, 2251, 2287, 2311, 2713, 2791, 2887, 3307, 3433, 3511, 3697, 3733, 3847, 4261, 4327, 4363, 4483, 4861, 4951, 5023, 5407, 5563, 5743, 6553, 6571, 6781, 6991, 7177, 7333

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

Cf. A034953.

Sequence in context: A142191 A086126 A023287 * A248431 A141919 A308797

Adjacent sequences: A203260 A203261 A203262 * A203264 A203265 A203266

Keyword

nonn

Author

Arkadiusz Wesolowski, Jan 13 2012

Status

approved