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 A285813 Let p_1
 0, 1, 1, 0, 1, 1, 2, 1, 1, 2, 1, 3, 2, 1, 4, 3, 6, 1, 1, 1, 1, 2, 1, 3, 2, 1, 2, 2, 1, 3, 2, 10, 1, 1, 1, 1, 4, 5, 1, 1, 1, 2, 2, 1, 5, 3, 6, 3, 1, 1, 1, 2, 1, 1, 2, 1, 9, 6, 0, 6, 2, 5, 2, 1, 1, 4, 2, 1, 7, 4, 4, 7, 1, 2, 8, 3, 7, 1, 2, 4, 1, 1, 1, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS The sequence of positions of zeros either grows very fast or is finite. We are inclined to the latter option (cf. our comments in A284919 and in A285770). By A284967, the first three positions of zeros are {4,59,434} and, according to the last calculations by Michel Marcus, no more positions up to 5*10^7. There are many more terms in A284919 than zeros in this sequence. The reason of this phenomenon is the following. In A284919, if n is not divisible by 3 and 2*n-3 is composite then 2*n+p is composite for every prime for which 2*n-p is prime. Indeed, for these 2*n all such primes p are in the interval (3, 2*n-3). Then either 2*n-p or 2*n+p should be divisible by 3, but 2*n-p is prime >3. So, 2*n+p is composite. LINKS MATHEMATICA Flatten@ Table[FirstPosition[#, p_ /; PrimeQ@ p] /. k_ /; MissingQ@ k -> {0} &@ Map[2 n + NestWhile[#/2 &, # - 1, EvenQ@ # &] &, Select[Prime@ Range@ PrimePi[2 n - 2], PrimeQ[2 n - #] &]], {n, 86}] (* Michael De Vlieger, Apr 27 2017, Version 10.2 *) PROG (PARI) oddp(n) = n/2^valuation(n, 2); a(n) = {i = 0; forprime(p=2, 2*n, if (isprime(2*n-p), i++; if (isprime(2*n+oddp(p-1)), return(i)); ); ); return(0); } \\ Michel Marcus, Apr 29 2017 CROSSREFS Cf. A284919, A284967, A285770. Sequence in context: A135062 A088428 A025838 * A236480 A236508 A239000 Adjacent sequences:  A285810 A285811 A285812 * A285814 A285815 A285816 KEYWORD nonn AUTHOR Vladimir Shevelev, Apr 27 2017 EXTENSIONS More terms from Michael De Vlieger, Apr 27 2017 STATUS approved

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Last modified January 20 02:13 EST 2019. Contains 319320 sequences. (Running on oeis4.)