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A006509 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)
16
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; text; internal format)
OFFSET

1,2

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).

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000

R. G. Wilson, Letter to N. J. A. Sloane with attachment, Jan 1989

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))];

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 (* Robert G. Wilson v, Apr 25 2006 *)

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

CROSSREFS

Cf. A005132, A093903. Zeros are in A112877. Sorted: A111338, A111339 (numbers missing from A006509).

Cf. A117128, A117129, A064365, A005132, A000040.

Sequence in context: A293666 A093903 A117128 * A258928 A144562 A102889

Adjacent sequences:  A006506 A006507 A006508 * A006510 A006511 A006512

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Jul 20 2001

Many more terms added by N. J. A. Sloane, Apr 20 2006, to show difference from A117128.

STATUS

approved

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Last modified October 21 23:02 EDT 2018. Contains 316431 sequences. (Running on oeis4.)