login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A064365 a(0) = 0; thereafter a(n) = a(n-1)-p(n) if positive and new, otherwise a(n) = a(n-1)+p(n), where p(n) is the n-th prime. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

'Recamán transform' (see A005132) of the prime sequence. Note that the definition permits repeated terms (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 = {2}; 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, 2, 70} ]; a

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, a-p), 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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 17 14:37 EST 2019. Contains 320220 sequences. (Running on oeis4.)