The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322161 Numbers k such that m = 8k^2 + 2k + 33 and 8m - 7 are both primes. 2
 1, 46, 58, 133, 145, 175, 208, 223, 241, 403, 430, 463, 526, 568, 808, 868, 985, 1015, 1021, 1105, 1120, 1360, 1465, 1501, 1600, 1918, 1978, 2236, 2350, 2413, 2908, 2965, 3043, 3211, 3265, 3523, 3556, 3568, 3601, 3721, 3811, 3868, 4066, 4291, 4300, 4336, 4831 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Rotkiewicz proved that if k is in this sequence, and m = 8k^2 + 2k + 33, then m*(8m - 7) is an octadecagonal Fermat pseudoprime to base 2 (A322160), and thus under Schinzel's Hypothesis H there are infinitely many decagonal Fermat pseudoprimes to base 2. The corresponding pseudoprimes are 14491, 2326319101, 5858192341, 160881885091, 227198832571, 481700815831, 960833787841, ... LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259. Wikipedia, Schinzel's Hypothesis H. EXAMPLE 1 is in the sequence since 8*1^2 + 2*1 + 33 = 43 and 8*43 - 7 = 337 are both primes. MATHEMATICA Select[Range[1000], PrimeQ[8#^2 + 2# + 33] && PrimeQ[64#^2 + 16# + 257]  &] PROG (PARI) isok(n) = isprime(m = 8*n^2+2*n+33) && isprime(8*m-7); \\ Michel Marcus, Nov 29 2018 CROSSREFS Cf. A001567, A051870, A322160. Sequence in context: A332952 A308099 A308252 * A039424 A043247 A044027 Adjacent sequences:  A322158 A322159 A322160 * A322162 A322163 A322164 KEYWORD nonn AUTHOR Amiram Eldar, Nov 29 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)