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A006509
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Cald's sequence: a(n+1)=a(n)-p(n) if new and >0, else a(n)+p(n) if new, otherwise 0, where p(n) = n-th prime.
(Formerly M2539)
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13
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1, 3, 6, 11, 4, 15, 2, 19, 38, 61, 32, 63, 26, 67, 24, 71, 18, 77, 16, 83, 12, 85, 164, 81, 170, 73, 174, 277, 384, 275, 162, 35, 166, 29, 168, 317, 468, 311, 148, 315, 142, 321, 140, 331, 138, 335, 136, 347, 124, 351, 122, 355, 116, 357, 106, 363, 100, 369, 98, 375, 94, 377, 84, 391, 80, 393, 76, 407, 70, 417, 68, 421, 62, 429, 56, 435, 52, 441, 44, 445, 36, 455, 34, 465, 898, 459, 902, 453, 910, 449, 912, 1379, 900, 413, 904, 405, 908, 399, 920, 397, 938, 1485, 928, 365, 934, 1505, 2082, 1495, 2088, 1489, 888, 281, 894, 1511, 892, 261, 0, 643, 1290, 637, 1296, 635, 1308, 631, 1314, 623, 1324, 615, 1334, 607, 1340
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| F. Cald, Problem 356, Franciscan order, J. Rec. Math., 7 (No. 4, 1974), 318; 10 (No. 1, 1974), 62-64.
"Cald's Sequence", Popular Computing (Calabasas, CA), Vol. 4 (No. 41, Aug 1976), pp. 16-17.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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MAPLE
| M1:=500000; a:=array(0..M1); have:=array(0..M1); a[0]:=1;
for n from 0 to M1 do have[n]:=0; od: have[0]:=1; have[1]:=1;
M2:=2000; nmax:=M2; for n from 1 to M2 do p:=ithprime(n); i:=a[n-1]-p; j:=a[n-1]+p;
if i >= 1 and have[i]=0 then a[n]:=i; have[i]:=1;
elif j <= M1 and have[j]=0 then a[n]:=j; have[j]:=1;
elif j <= M1 then a[n]:=0; else nmax:=n-1; break; fi; od:
# To get A006509:
[seq(a[n], n=0..M2)];
# To get A112877 (off by 1 because of different offset in A006509):
zzz:=[]; for n from 0 to nmax do if a[n]=0 then zzz:=[op(zzz), n]; fi; od: [seq(zzz[i], i=1..nops(zzz))];
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MATHEMATICA
| lst = {1}; f := Block[{b = Last@lst, p = Prime@ Length@lst}, If[b > p && !MemberQ[lst, b - p], AppendTo[lst, b - p], If[ !MemberQ[lst, b + p], AppendTo[lst, b + p], AppendTo[lst, 0]] ]]; Do[f, {n, 60}]; lst (from Robert G. Wilson v (rgwv(at)rgwv.com), Apr 25 2006)
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PROG
| (Haskell)
a006509 n = a006509_list !! (n-1)
a006509_list = 1 : f [1] a000040_list where
f xs'@(x:_) (p:ps) | x' > 0 && x' `notElem` xs = x' : f (x':xs) ps
| x'' `notElem` xs = x'' : f (x'':xs) ps
| otherwise = 0 : f (0:xs) ps
where x' = x - p; x'' = x + p
-- Reinhard Zumkeller, Oct 17 2011
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CROSSREFS
| Cf. A005132, A093903. Zeros are in A112877. Sorted: A111338, A111339.
Cf. A117128, A117129, A064365.
Cf. A000040.
Sequence in context: A110080 A093903 A117128 * A144562 A102889 A183543
Adjacent sequences: A006506 A006507 A006508 * A006510 A006511 A006512
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Jul 20 2001
Many more terms added by N. J. A. Sloane (njas(AT)research.att.com), Apr 20 2006, to show difference from A117128.
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