

A064365


a(0) = 0; thereafter a(n) = a(n1)prime(n) if positive and new, otherwise a(n) = a(n1)+prime(n), where prime(n) is the nth prime.


6



0, 2, 5, 10, 3, 14, 1, 18, 37, 60, 31, 62, 25, 66, 23, 70, 17, 76, 15, 82, 11, 84, 163, 80, 169, 72, 173, 276, 383, 274, 161, 34, 165, 28, 167, 316, 467, 310, 147, 314, 141, 320, 139, 330, 137, 334, 135, 346, 123, 350, 121, 354, 115, 356, 105, 362, 99, 368, 97, 374, 93
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OFFSET

0,2


COMMENTS

'Recamán transform' (see A005132) of the prime sequence. Note that the definition permits repeated terms [though only by addition] (and there are many repeated terms, just as there are in A005132).
Does every positive integer appear in the sequence? This seems unlikely, since 4 has not appeared in 70000 terms.
Note: this is similar to Clark Kimberling's A022831, except in the latter sequence the words 'and new' have been omitted.
The smallest numbers not occurring in the first million terms: 4, 6, 7, 12, 13, 16, 19, 20, 21, 22, 24, 26, 27, 29, 30, 32, 36, 39, 41, 42.  Reinhard Zumkeller, Apr 26 2012


LINKS

N. J. A. Sloane, First 70000 terms
Index entries for sequences related to Recamán's sequence


FORMULA

a(n) = A117128(n)  1.  Thomas Ordowski, Dec 05 2016


EXAMPLE

To find a(9) we try subtracting the 9th prime, which is 23, from a(8), which is 37. 37  23 = 14, but 14 is already in the sequence (it is a(5)), so we must add. a(9) = 37 + 23 = 60.


MATHEMATICA

a = {0}; Do[ If[ a[ [ 1 ] ]  Prime[ n ] > 0 && Position[ a, a[ [ 1 ] ]  Prime[ n ] ] == {}, a = Append[ a, a[ [ 1 ] ]  Prime[ n ] ], a = Append[ a, a[ [ 1 ] ] + Prime[ n ] ] ], {n, 1, 70} ]; a (* Modified by Ivan N. Ianakiev, Aug 05 2019, to accommodate the new initial term of a(0). *)


PROG

(PARI) A064365(N, s/*=1 to print all terms*/)={ my(a=0, u=0); N & forprime(p=1, prime(N), s & print1(a", "); u=bitor(u, 2^a+=if(a<=p  bittest(u, ap), p, p))); a} \\ M. F. Hasler, Mar 07 2012
(Haskell)
import Data.Set (singleton, notMember, insert)
a064365 n = a064365_list !! n
a064365_list = 0 : f 0 a000040_list (singleton 0) where
f x (p:ps) s  x' > 0 && x' `notMember` s = x' : f x' ps (insert x' s)
 otherwise = xp : f xp ps (insert xp s)
where x' = x  p; xp = x + p
 Reinhard Zumkeller, Apr 26 2012


CROSSREFS

Cf. A005132, A022831, A117128.
Sequence in context: A059955 A099796 A022831 * A177356 A078322 A252867
Adjacent sequences: A064362 A064363 A064364 * A064366 A064367 A064368


KEYWORD

nonn,easy,nice,look,hear


AUTHOR

Neil Fernandez, Sep 25 2001


EXTENSIONS

More terms from Robert G. Wilson v, Sep 26 2001
Further terms from N. J. A. Sloane, Feb 10 2002
Added initial term a(0)=0, in analogy with A128204, A005132, A053461, A117073/A078783.  M. F. Hasler, Mar 07 2012


STATUS

approved



