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 A262627 Minimal nested base-2 palindromic primes with seed 0. 19
 0, 101, 11001010011, 101100101001101, 10101011001010011010101, 111010101100101001101010111, 1111101010110010100110101011111, 101111111010101100101001101010111111101, 110101111111010101100101001101010111111101011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Using only base-2 digits 0 and 1, let s be a palindrome and put a(1) = s. Let a(2) be the least palindromic prime having s in the middle; for n > 2, let a(n) be the least palindromic prime have a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested base-2 palindromic primes with seed s -- a(1) being not prime, of course. Guide to related sequences base  seed   base-b repr.    base-10 repr. 2         0      A262627        A262628 2         1      A262629        A262630 3         1      A262631        A262632 4         0      A262633        A262634 4         1      A262635        A262636 4         2      A262637        A262638 4         3      A262639        A262640 5         1      A262641        A262642 5         3      A262643        A262644 6         0      A262645        A262646 6         1      A262647        A262648 6         2      A262649        A262650 6         3      A262651        A262652 6         4      A262653        A262654 6         5      A262655        A262656 7         1      A262657        A262658 8         0      A262659        A262660 8         1      A262661        A262662 10        0      A261881        A261881 10        1      A261818        A261818 LINKS Clark Kimberling, Table of n, a(n) for n = 1..300 EXAMPLE a(3) = 11001010011 =A117697(15) is the least prime having a(2) = 101 in its middle. Triangular format:                0               101           11001010011         101100101001101     10101011001010011010101   111010101100101001101010111 1111101010110010100110101011111 MATHEMATICA s = {0}; base = 2; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &]; AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262627 *) Map[FromDigits[ToString[#], base] &, s]  (* A262628 *) (* Peter J. C. Moses, Sep 01 2015 *) CROSSREFS Cf. A117697, A261881 (base 10), A262628-A262662. Sequence in context: A138826 A292686 A138720 * A259199 A006064 A230304 Adjacent sequences:  A262624 A262625 A262626 * A262628 A262629 A262630 KEYWORD nonn,base AUTHOR Clark Kimberling, Oct 02 2015 STATUS approved

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Last modified October 19 11:00 EDT 2019. Contains 328216 sequences. (Running on oeis4.)