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 A211681 Numbers such that all the substrings of length <= 2 are primes. 55
 2, 3, 5, 7, 23, 37, 53, 73, 237, 373, 537, 737, 2373, 3737, 5373, 7373, 23737, 37373, 53737, 73737, 237373, 373737, 537373, 737373, 2373737, 3737373, 5373737, 7373737, 23737373, 37373737, 53737373, 73737373, 237373737, 373737373, 537373737, 737373737 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The terms are primes for n= 1, 2, 3, 4, 5, 6, 7, 8, 10, 21, 23, 27, 31, 43, 45, 60, 67, 82, 91,.... The further terms with index 92, 93, 94, 96, 99 are composite. For the subsequence with prime terms see A211682. Cf. A213299 for the partial sums. LINKS Hieronymus Fischer, Table of n, a(n) for n = 1..100 FORMULA a(1+8*k) =  2*10^(2k) + 37*sum_{j=0..k-1} 10^(2j), a(2+8*k) =  3*10^(2k) + 73*sum_{j=0..k-1} 10^(2j), a(3+8*k) =  5*10^(2k) + 37*sum_{j=0..k-1} 10^(2j), a(4+8*k) =  7*10^(2k) + 37*sum_{j=0..k-1} 10^(2j), a(5+8*k) = 23*10^(2k) + 73*sum_{j=0..k-1} 10^(2j), a(6+8*k) = 37*10^(2k) + 37*sum_{j=0..k-1} 10^(2j), a(7+8*k) = 53*10^(2k) + 73*sum_{j=0..k-1} 10^(2j), a(8+8*k) = 73*10^(2k) + 73*sum_{j=0..k-1} 10^(2j), for k>=0. a(n) = ((2*n+7) mod 8 + d(n+4) - d(n+3))*10^d(n-1) + floor((37+36*(d(n+2)-d(n+1))*10^d(n-1)/99), where d(n)= floor(n/4). Recursion for n>8: a(n) = 10*(1+a(n-4)) - a(n-4) mod 10. G.f.: (2*x*(1+x^10) + 3*x^2*(1 + x^3 + x^5 + x^6) + 5*x^3*(1+x^6) + 7*x^4*(1+x^2))/((1-10*x^4)*(1-x^8)). EXAMPLE a(11)=537, since all substrings of length <= 2 are primes (5, 3, 7, 53 and 37). a(21)=237373, the substrings of length <= 2 are 2, 3, 7, 23, 37, 73. CROSSREFS Cf. A019546, A035232, A039996, A046034, A085823, A211682, A213299. Sequence in context: A019546 A104179 A096148 * A124674 A177061 A020994 Adjacent sequences:  A211678 A211679 A211680 * A211682 A211683 A211684 KEYWORD nonn,base,easy AUTHOR Hieronymus Fischer, Apr 30 2012 EXTENSIONS Typo in g.f. corrected, Hieronymus Fischer, Sep 03 2012 STATUS approved

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