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A258483 Numbers n such that partial sums of the n-th row of Pascal's triangle (A007318) are all nonprime.

%I A258483 #28 Apr 07 2025 16:45:03
%S A258483 0,9,29,33,34,37,38,39,41,45,49,65,67,69,73,74,77,85,86,92,97,98,101,
%T A258483 105,113,114,115,117,118,121,129,133,134,137,139,141,145,146,151,154,
%U A258483 155,158,160,161,164,165,170,173,177,182,185,186,193,194,195,199,202,205,206,209,213,214,225,227,229,230,234,241,247,257,258,259,261,263,265,266,269,272,273,277,281
%N A258483 Numbers n such that partial sums of the n-th row of Pascal's triangle (A007318) are all nonprime.
%C A258483 It appears that a(n) ~ c*n, as n goes to infinity, where c is constant < 2.17. For heuristic argument, see _Robert Israel_ link.
%H A258483 Peter J. C. Moses, <a href="/A258483/b258483.txt">Table of n, a(n) for n = 0..2499</a>
%H A258483 Robert Israel, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-June/014940.html">Re: a surprising property</a>, SeqFan list, Jun 01 2015.
%p A258483 T:= <1>:
%p A258483 res:= 0:
%p A258483 for n from 1 to 1000 do
%p A258483   T:= <1, T[1..-2] + T[2..-1], 2^n>;
%p A258483   if not ormap(isprime,T) then res:= res, n fi
%p A258483 od:
%p A258483 res; # _Robert Israel_, Jun 04 2015
%o A258483 (PARI) isok(n) = {my(s = 0); for (k=0, n, s += binomial(n, k); if (isprime(s), return (0))); return (1);} \\ _Michel Marcus_, May 31 2015
%Y A258483 Cf. A007318, A008949, A258126, A258127.
%K A258483 nonn
%O A258483 0,2
%A A258483 _Vladimir Shevelev_, May 31 2015