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 A242786 Least prime p such that p^n and p^n+1 have the same number of prime factors (counted with multiplicity) or 0 if no such number exists. 2
 2, 3, 3, 43, 7, 41, 23, 643, 17, 557, 251, 13183, 1999, 10007, 107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also least number k > 1 such that k^n and k^n+1 have the same number of prime factors. Since the data values are prime, p^n and p^n+1 have n prime factors. a(21) = 1151. a(17) = 5119. - Michel Marcus, Sep 21 2018 a(16) > 10^6; a(18) = 33577; a(19) = 48383. - Jon E. Schoenfield, Sep 22 2018 a(20) > 10^6. - Jon E. Schoenfield, Sep 28 2018 a(16) <= 206874667. - Daniel Suteu, Dec 09 2022 LINKS Table of n, a(n) for n=1..15. EXAMPLE 2^3 = 8 and 2^3 + 1 = 9 do not have the same number of prime factors. 3^3 = 27 and 3^3 + 1 = 28 both have 3 prime factors (27 = 3*3*3 and 28 = 7*2*2). Thus, a(3) = 3. PROG (PARI) a(n)=forprime(p=1, oo, if(bigomega(p^n+1)==n, return(p))); \\ Michel Marcus, Sep 21 2018 CROSSREFS Cf. A001222 (bigomega), A241793. Sequence in context: A096502 A101462 A345751 * A214219 A365223 A323340 Adjacent sequences: A242783 A242784 A242785 * A242787 A242788 A242789 KEYWORD nonn,more,hard AUTHOR Derek Orr, May 22 2014 EXTENSIONS Data restricted to known terms by Michel Marcus, Sep 21 2018 a(12) & a(14) from Michel Marcus, Sep 21 2018 STATUS approved

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Last modified September 17 18:39 EDT 2024. Contains 375990 sequences. (Running on oeis4.)