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 A085061 a(0) = 1; a(n+1) is the largest positive number (of at most two) such that abs(a(n) - a(n+1)) is the smallest prime not occurring earlier as difference of successive terms and a(n) + a(n+1) is composite. 2
 1, 3, 6, 19, 14, 21, 4, 23, 34, 57, 86, 117, 158, 121, 164, 211, 264, 205, 266, 199, 270, 353, 426, 505, 594, 691, 590, 487, 594, 485, 598, 725, 856, 993, 1132, 1281, 1124, 973, 1136, 1303, 1476, 1655, 1474, 1665, 1858, 2055, 2254, 2465, 2242, 2469, 2240, 2473 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Conjecture 1: a(n+5) > a(n). Conjecture 2: There are no numbers which occur more than once. LINKS EXAMPLE a(4) = 14; the smallest prime not occurring earlier as difference of successive terms is 7; there are two numbers x such that abs(14 - x) = 7 and 14 + x is composite, namely x = 7 and x = 21. The larger of these numbers is 21, so a(5) = 21. a(5) = 21; the smallest primes not occurring earlier as difference of successive terms are 11 and 17; there are two numbers x such that abs(21 - x) = 11, namely x = 10 and x = 32, but neither 21 + 10 = 31 nor 21 + 32 = 53 is composite; there are two numbers x such that abs(21 - x) = 17, namely x = 4 and x = 38 and 21 + 38 = 59 is not composite while 21 + 4 = 25 is composite; hence a(6) = 4. PROG (PARI) {in(n, v)=local(j, s, b); j=1; s=matsize(v)[2]; b=1; while(b&&j<=s, if(n==v[j], b=0, j++)); !b} {print1(a=1, ", "); v=[]; for(n=1, 51, p=2; t=1; while(t>0, if(in(p, v), p=nextprime(p+1), if(!isprime(2*a+p), t=0; b=a+p, if(p

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Last modified April 10 21:21 EDT 2021. Contains 342856 sequences. (Running on oeis4.)