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 A178102 2^(absolute difference between prime factors of n-th semiprime) mod (n-th semiprime). 2
 1, 2, 1, 8, 4, 4, 16, 6, 1, 20, 25, 26, 4, 10, 10, 12, 1, 13, 9, 43, 44, 16, 61, 52, 56, 16, 62, 16, 22, 22, 64, 70, 24, 44, 80, 28, 59, 30, 72, 1, 92, 31, 97, 106, 34, 106, 36, 4, 136, 110, 64, 40, 40, 9, 42, 1, 133, 134, 46, 81, 64, 146, 151, 152, 121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Robert Israel, Apr 05 2020: (Start) If A001358(n) = 2*p, then a(n) = (p+1)/2 if p == 3 (mod 4), or (3*p+1)/2 if p == 1 (mod 4). If A001358(n) = 3*p with p > 3, then a(n) = (3*p+1)/4 if p == 1 (mod 4), or (9*p+1)/4 if p == 3 (mod 4). (End) LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(1)=1 because the first semiprime is 4=2*2 and 2^(2-2) mod 4 = 1. a(11)=25 because the 11th semiprime is 33=3*11 and 2^(11-3) mod 33 = 25. MAPLE b:= proc(n) option remember; local k; if n=1 then 4 else for k from b(n-1)+1 while isprime(k) or add (i[2], i=ifactors(k)[2])<>2 do od; k fi end: a:= proc(n) local l; l:= ifactors (b(n))[2]; if nops (l)=1 then 1 else 2 &^ abs(l[1][1]-l[2][1]) mod b(n) fi end: seq (a(n), n=1..65); MATHEMATICA Mod[2^Differences[FactorInteger[#][[All, 1]]], #]&/@Select[Range[300], PrimeOmega[ #] == 2&]/.{}->1//Flatten (* Harvey P. Dale, Dec 25 2018 *) CROSSREFS Cf. A000079, A001358. Sequence in context: A308695 A278111 A223550 * A245836 A368386 A135520 Adjacent sequences: A178099 A178100 A178101 * A178103 A178104 A178105 KEYWORD nonn,look AUTHOR Juri-Stepan Gerasimov, Dec 16 2010 EXTENSIONS Edited by Alois P. Heinz, Dec 17 2010 STATUS approved

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Last modified September 13 10:55 EDT 2024. Contains 375904 sequences. (Running on oeis4.)