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A103781 Sum of any four successive terms is prime, a(1)=a(2)=0,a(3)=1. 1
0, 0, 1, 1, 1, 2, 3, 5, 3, 6, 5, 9, 9, 8, 11, 13, 11, 12, 17, 19, 13, 18, 21, 21, 19, 22, 27, 29, 23, 24, 31, 31, 27, 38, 35, 37, 29, 48, 37, 43, 35, 52, 43, 49, 37, 62, 45, 53, 39, 74, 57, 57, 41, 78, 63, 59, 51, 84, 69, 65, 53, 90, 73, 67, 63, 104, 77, 69, 67, 118, 83, 79, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

The sequence depends on initial three terms. Assuming no negative sequence we have ten distinct sets of first terms. We may denote them in short as s000,s001(=this sequence),s010,s011,s100,s101,s110,s002,s020 and s200. These sequences do not merge into each other, but maintain their individuality. E.g. terms nos. 97-100 are: {128,107,162,144},{127,107,162,145},{127,107,163,144}, 126,107,163,145},{127,108,162,144},{126,108,162,145},{126,108,163,144},{126,107,162,146},{126,107,164,144},{126,109,162,144}, for above mentioned sequences, respectively. The same is true for the case of "sum of three successive terms" A073737, where we have six distinct sets of first terms s00,s01,s10,s11(=A073737),s02 and s20.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

(*seed*)b4 = {0, 0, 1}; Do[x = Prime[n] - (b4[[ -1]] + b4[[ -2]] + b4[[ -3]]); b4 = Append[b4, x], {n, 1, 200}]; b4

nxt[{a_, b_, c_}] := {b, c, NextPrime[a + b + c] - (a+b + c)}; NestList[nxt, {0, 0, 1}, 100][[All, 1]](* Harvey P. Dale, Sep 20 2022 *)

CROSSREFS

Cf. A073737.

Sequence in context: A114230 A209753 A185191 * A095244 A147593 A108396

Adjacent sequences: A103778 A103779 A103780 * A103782 A103783 A103784

KEYWORD

nonn

AUTHOR

Zak Seidov, Feb 15 2005

STATUS

approved

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Last modified December 2 17:51 EST 2022. Contains 358510 sequences. (Running on oeis4.)