

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
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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. 97100 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



