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 A203263 Primes p such that 29*p + 14 and 41*p + 20 are also prime. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 12 02:35 EDT 2024. Contains 375842 sequences. (Running on oeis4.)