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 A286982 Smallest nonnegative k such that (1 + k)^(2^n) + k is not prime and all (1 + k)^(2^j) + k, for 0 <= j < n, are primes. 1
 6, 3, 5, 2, 1, 54131988 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE a(1) = 6 because (1 + 6)^(2^1) + 6 = 55 is semiprime and (1 + 6)^(2^0) + 6 = 13 is prime; a(2) = 3 because (1 + 3)^(2^2) + 3 = 259 is semiprime and both (1 + 3)^(2^0) + 3 = 7 and (1 + 3)^(2^1) + 3 = 19 are primes; a(3) = 5 because (1 + 5)^(2^3) + 5 = 167921 is semiprime and (1 + 5)^(2^0) + 5 = 11, (1 + 5)^(2^1) + 5 = 41 and (1 + 5)^(2^2) + 5 = 1301 are all primes; a(4) = 2 because (1 + 2)^(2^4) + 2 = 43046723 is semiprime and (1 + 2)^(2^0) + 2 = 5, (1 + 2)^(2^1) + 2 = 11, (1 + 2)^(2^2) + 2 = 83 and (1 + 2)^(2^3) + 2 = 6563 are all primes; a(5) = 1 because (1 + 1)^(2^5) + 1 = 4294967297 is semiprime and (1 + 1)^(2^0) + 1 = 3, (1 + 1)^(2^1) + 1 = 5, (1 + 1)^(2^2) + 1 = 17, (1 + 1)^(2^3) + 1 = 257 and (1 + 1)^(2^4) + 1 = 65537 are fix known Fermat primes (A019434); a(6) = 54131988 because (1 + 54131988)^(2^6) + 54131988 is composite and (1 + 54131988)^(2^0) + 54131988 = 108263977, (1 + 54131988)^(2^1) + 54131988 = 2930272287228109, (1 + 54131988)^(2^2) + 54131988 =  8586495360054127683625679378629, (1 + 54131988)^(2^3) + 54131988 = 73727902568231063808600888120898279950965368674840612135914869, (1 + 54131988)^(2^4) + 54131988 and (1 + 54131988)^(2^5) + 54131988 are all primes. MATHEMATICA a[n_] := Block[{k = 1}, While[PrimeQ[(1 + k)^(2^n) + k] || ! AllTrue[(1 + k)^(2^Range[0, n-1]) + k, PrimeQ], k++]; k]; Array[a, 5] (* Giovanni Resta, May 30 2017 *) CROSSREFS Cf. A019434, A047845, A057726, A160027, A286680. Sequence in context: A305187 A065418 A228725 * A153595 A195482 A298529 Adjacent sequences:  A286979 A286980 A286981 * A286983 A286984 A286985 KEYWORD nonn,more AUTHOR Juri-Stepan Gerasimov, May 12 2017 EXTENSIONS a(6) from Robert G. Wilson v, May 14 2017 STATUS approved

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Last modified November 14 22:32 EST 2019. Contains 329134 sequences. (Running on oeis4.)