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 A237117 Remainder mod p of the smallest semiprime of the form k^p+1, where p = prime(n); or -1 if no such semiprime exists. 2
 0, 0, 3, 3, 3, 3, 3, 3, 3, 24, 3, 17, 26, 3, 7, 11, 7, 3, 11, 47, 19, 3, 5, 17, 71, 3, 97, 7, 13, 32, 3, 97, 67, 31, 17, 48, 23, 53, 3, 17, 157, 108, 3, 13, 53, 3, 67, 47, 23, 97, 88, 127, 106, 17, 37, 97, 145, 89, 73, 53, 173, 11, 17, 106, 3, 17, 47, 323, 3, 112, 23, 314, 37, 29, 331, 174, 266, 194, 226, 397, 29, 16, 176, 45, 44, 152, 373, 349, 101, 143, 53, 386, 133, 29, 345, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS It appears that a(n) > 0 for all n > 2. See the comments in A237114. LINKS Eric Weisstein's World of Mathematics, Semiprime Wikipedia, Semiprime FORMULA a(n) = A237114(n) mod prime(n) = A237115(n) mod prime(n), if A237114(n)>0. EXAMPLE Prime(2)=3 and the smallest semiprime of the form k^3+1 is 2^3+1 = 9 = 3*3, so a(2) = 9 mod 3 = 0. Prime(3)=5 and the smallest semiprime of the form k^5+1 is 2^5+1 = 33 = 3*11, so a(3) = 33 mod 5 = 3. MATHEMATICA L = {0}; Do[p = Prime[k]; n = 1; q = Prime[n] - 1; cp = (q^p + 1)/(q + 1); While[! PrimeQ[cp], n = n + 1; q = Prime[n] - 1; cp = (q^p + 1)/(q + 1)]; L = Append[L, Mod[q^p + 1, p]], {k, 2, 87}]; L CROSSREFS Cf. A001358, A006881, A103795, A123627, A123628, A237040, A237114, A237115, A237116. Sequence in context: A210745 A187471 A083565 * A247970 A063438 A276870 Adjacent sequences:  A237114 A237115 A237116 * A237118 A237119 A237120 KEYWORD nonn AUTHOR Jonathan Sondow, Feb 06 2014 STATUS approved

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Last modified January 24 17:24 EST 2021. Contains 340411 sequences. (Running on oeis4.)