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%I #25 Apr 23 2015 09:49:38
%S 2,3,7,13,47,61,73,107,167,179,313,347,421,479,719,863,1153,1213,1283,
%T 1307,1523,3467,3733,4007,4621,4787,5087,5113,5413,7523,7703,9817,
%U 10333,12347,12539,13381,17027,18553,19717,19813,23399,26003,31873,36097,38833
%N Primes which are not the sum of two or more consecutive nonprime numbers.
%C Numbers n such that A257392(n) = 0.
%H Robert Israel, <a href="/A257393/b257393.txt">Table of n, a(n) for n = 1..209</a>
%e 2 and 3 are in this sequence because nonnegative nonprime(1) + nonnegative nonprime(2) = 0 + 1 = 1 < 2 and nonnegative nonprime(2) + nonnegative nonprime(3) = 1 + 4 = 5 > 3 where 2, 3 are primes.
%p N:= 5000: # to get all terms <= N
%p Primes:= select(isprime,{2,seq(2*i+1, i=1..floor((N-1)/2))}):
%p Nonprimes:= sort(convert({$1..N} minus Primes, list)):
%p nnp:= nops(Nonprimes):
%p PSums:= [0,op(ListTools[PartialSums](Nonprimes))]:
%p A:= Primes:
%p mA:= max(A):
%p for i from 1 to nnp do
%p for j from i+2 to nnp+1 while PSums[j] - PSums[i] <= mA do od;
%p A:= A minus {seq(PSums[k]-PSums[i],k=i+2..j-1)};
%p od od:
%p A;
%p # if using Maple 11 or earlier, uncomment the next line
%p # sort(convert(A,list)); # _Robert Israel_, Apr 21 2015
%t lim = 1000; s = {1}~Join~Select[Range@lim, CompositeQ]; Complement[Prime@ Range[PrimePi@ lim], DeleteDuplicates@ Sort@ Flatten[Plus @@@ Partition[s, #, 1] & /@ Range[lim - PrimePi@ lim]]] (* _Michael De Vlieger_, Apr 21 2015 *)
%Y Cf. A257392, A018252, A141468.
%K nonn,easy
%O 1,1
%A _Juri-Stepan Gerasimov_, Apr 21 2015
%E a(7) - a(26) from _Michael De Vlieger_, Apr 21 2015
%E a(27) - a(45) from _Robert Israel_, Apr 21 2015
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