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 A340707 a(n) = (prevprime(2^n) + nextprime(2^n))/2 - 2^n where prevprime(n) = A151799(n) and nextprime(n) = A151800(n). 2
 0, 1, -1, 2, 0, 1, -2, 3, 2, -2, 0, 8, 12, -8, -7, 14, -1, 10, 2, 4, 6, -3, 20, -2, 5, -5, -27, 4, -16, 5, 5, 4, -8, 11, 13, -8, -19, 8, -36, 3, 2, -14, -5, 2, -3, -55, -19, -6, 14, -54, -13, -53, 63, -26, 38, -2, 21, 38, -30, 7, 39, 2, -23, 41, 2, -8, 5, 5, -5, -110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,4 COMMENTS a(n) > 0 if the difference nextprime(2^n) - 2^n = A013597(n) is greater than the difference 2^n - previousprime(2^n) = A013603(n). LINKS Hugo Pfoertner, Table of n, a(n) for n = 2..5000 (from T. D. Noe's b-files in A013597 and A013603). FORMULA a(n) = (A013597(n) - A013603(n))/2. a(A226178(n)) = 0. EXAMPLE a(4) = -1: 2^4 = 16, (13 + 17 - 32)/2 = -1; a(5) = 2: 2^5 = 32, (31 + 37 - 64)/2 = 2; a(6) = 0: 2^6 = 64, (61 + 67 - 128)/2 = 0. MAPLE a:= (p-> (nextprime(p)+prevprime(p))/2-p)(2^n): seq(a(n), n=2..75);  # Alois P. Heinz, Jan 29 2021 MATHEMATICA Array[(NextPrime[2^#] + NextPrime[2^#, -1] - 2^(# + 1))/2 &, 60, 2] (* Michael De Vlieger, Aug 07 2022 *) PROG (PARI) for(k=2, 71, my(p2=2^k, pp=precprime(p2), pn=nextprime(p2)); if(print1((pp+pn-2*p2)/2", "))) CROSSREFS Cf. A151799, A151800, A013597, A013603, A058249, A226178. Sequence in context: A049262 A145201 A323671 * A284265 A119464 A214568 Adjacent sequences:  A340704 A340705 A340706 * A340708 A340709 A340710 KEYWORD sign,changed AUTHOR Hugo Pfoertner, Jan 29 2021 EXTENSIONS Name made more precise by Peter Luschny, Aug 08 2022 STATUS approved

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Last modified August 11 00:55 EDT 2022. Contains 356046 sequences. (Running on oeis4.)