

A108348


Numbers of the form p^k + p^(k1) + ... + 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
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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<n, m++; forprime(p=2, m, if( m%p==1 && m*(p1)==p^round(log(m*(p1))/log(p))1, a=concat(a, m); next(2)) )); a }; a=A108348(1000) \\ M. F. Hasler
(GAP) SumNum := function ( FNum) local a, ap, b, bp, at, bt; a := 2; repeat at := 1; ap := 1; repeat at := at + a^ap; b := 2; repeat bt := 1; bp := 1; repeat bt := bt + b^bp; if at = bt and bp > 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 !! (n1)
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



