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 A268140 Smallest prime followed by at least 2^n nonprimes. 1
 3, 7, 23, 113, 523, 1327, 31397, 1357201, 436273009, 304599508537, 1693182318746371 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(16) <= 1931*A034386(1933)/7230 - 30244 (see J. K. Andersen link). Subsequence of A002386. - Chai Wah Wu, Feb 15 2016 From Chai Wah Wu, Jun 26 2019: (Start) Upper bounds derived from data in http://www.trnicely.net/index.html#TPG: a(11) <= 3001549619028223830552751967 a(12) <= 8298167160043173312303446808147809006055739815894846173 a(13) <= 293703234068022590158723766104419463425709075574811762098588798217895728858676728143227 a(14) <= 650094367*A034396(491)/2310 - 8936 a(15) <= 43882589*A034386(1063)/210 - 28456 a(17) <= 949*A034386(4691)/210 - 65386 a(18) <= 1111111111111111111*A034386(9293)/75201696570 - 138310 a(19) <= A034386(24137)/2310 - 311774 a(20) <= 587*A034386(43103)/2310 - 455704 a(21) <= A034386(90823)/510510 - 1065962 a(22) <= A034386(230077)/2229464046810 - 3131794 (End) LINKS Jens Kruse Andersen, Maximal Prime Gaps EXAMPLE 3 is the smallest prime followed by 1 composite number, 7 is the smallest prime followed by 2 or more composite numbers, 23 is the smallest prime followed by 4 or more composite numbers, 113 is the smallest prime followed by 8 or more composite numbers. MATHEMATICA Table[p = 2; While[NextPrime@ p - p <= 2^n, p = NextPrime@ p]; p, {n, 0, 7}] (* Michael De Vlieger, Jan 27 2016 *) PROG (PARI) a(n) = {my(p = 2); while(((q=nextprime(p+1)) - p) < 2^n+1, p = q); p; } \\ Michel Marcus, Jan 27 2016 (Python) from sympy import isprime def A268140(n):     p, n2 = 2, 2**n+1     while True:         for i in range(1, n2):             if isprime(p+i):                 p += i                 break         else:             return p # Chai Wah Wu, Feb 15 2016 CROSSREFS Cf. A000040, A002386, A053976. Sequence in context: A080077 A096318 A299404 * A133788 A120271 A145938 Adjacent sequences:  A268137 A268138 A268139 * A268141 A268142 A268143 KEYWORD nonn,hard,more AUTHOR Alex Ratushnyak, Jan 27 2016 EXTENSIONS a(8)-a(10) taken from J. K. Andersen's Maximal Prime Gaps webpage by Chai Wah Wu, Feb 15 2016 STATUS approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)