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 A329875 a(1) = 1, for n > 0, a(n+1) is the least prime number > a(n) whose binary expansion ends with the binary expansion of a(n). 1
 1, 3, 7, 23, 151, 919, 8087, 90007, 2449303, 6643607, 115695511, 786784151, 2934267799, 183322894231, 1007956615063, 4306491498391, 101063514742679, 2634338305138583, 106217129734659991, 2267944950872498071, 69137392218069622679, 2504107609947730435991 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is a binary variant of A053582. Dirichlet's theorem on arithmetic progressions guaranties that this sequence is infinite. We can build a similar sequence for any base b > 1 and any starting value coprime to b. LINKS Table of n, a(n) for n=1..22. EXAMPLE The first terms, alongside their binary representations, are: n a(n) bin(a(n)) - ------- ---------------------- 1 1 1 2 3 11 3 7 111 4 23 10111 5 151 10010111 6 919 1110010111 7 8087 1111110010111 8 90007 10101111110010111 9 2449303 1001010101111110010111 PROG (PARI) print1 (v=1); for (n=2, 22, forstep (w=v+s=(b=2)^#digits(v, b), oo, s, if (isprime(w), print1 (", "v=w); break))) CROSSREFS Cf. A053582, A329877. Sequence in context: A133788 A120271 A145938 * A048721 A113824 A121883 Adjacent sequences: A329872 A329873 A329874 * A329876 A329877 A329878 KEYWORD nonn,base AUTHOR Rémy Sigrist, Nov 23 2019 STATUS approved

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Last modified September 19 02:20 EDT 2024. Contains 376003 sequences. (Running on oeis4.)