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 A108348 Numbers of the form p^k + p^(k-1) + ... + p + 1 (where p is a prime and k>=0) in ascending order. 3
 1, 3, 4, 6, 7, 8, 12, 13, 14, 15, 18, 20, 24, 30, 31, 32, 38, 40, 42, 44, 48, 54, 57, 60, 62, 63, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 121, 127, 128, 132, 133, 138, 140, 150, 152, 156, 158, 164, 168, 174, 180, 182, 183, 192, 194, 198, 200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A proper subset of A002191 (e.g. 28 is in A002191, but not in this sequence). a(15)=31 admits two representations: 31=2^4+2^3+2^2+2+1=5^2+5+1. Are there other numbers with two or more representation? I have checked all the sums of primes up to prime number 56873 to a sum total >= 10^100 and have not come across another number that has multiple representations. - Patrick Schutte (patrick(AT)onyxsa.co.za), Mar 28 2007 LINKS M. F. Hasler, Table of n, a(n) for n = 1..1000 EXAMPLE a(2)=3=2+1 since a(1)=1 and 2 is not expressible in the required form. PROG (PARI) A108348(n)={ local(m=1, a=[m]); while( #a 1 and a <> b then Print("a ", a, " ap ", ap, " at ", at, " "); Print("b ", b, " bp ", bp, " bt ", bt, " "); Print("---------------- "); fi; bp := bp + 1; until bt > at; b := NextPrime(b); until b >=a; ap := ap + 1; until at > 10^100; a := NextPrime(a); until a >FNum; end; # Patrick Schutte (patrick(AT)onyxsa.co.za), Mar 28 2007 (Haskell) a108348 n = a108348_list !! (n-1) a108348_list = 1 : f [2..] where    f (x:xs) = g a000040_list where      g (p:ps) = h 0 \$ map ((`div` (p - 1)) . subtract 1) \$                           iterate (* p) (p ^ 2) where        h i (pp:pps) | pp > x    = if i == 0 then f xs else g ps                     | pp < x    = h 1 pps                     | otherwise = x : f xs -- Reinhard Zumkeller, Nov 26 2013 CROSSREFS Cf. A002191. Cf. A000040, A090503. Sequence in context: A007609 A285703 A002191 * A085149 A239458 A007370 Adjacent sequences:  A108345 A108346 A108347 * A108349 A108350 A108351 KEYWORD nonn AUTHOR Franz Vrabec, Jul 01 2005 STATUS approved

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Last modified October 22 17:39 EDT 2019. Contains 328319 sequences. (Running on oeis4.)