A257393 Primes which are not the sum of two or more consecutive nonprime numbers.

2, 3, 7, 13, 47, 61, 73, 107, 167, 179, 313, 347, 421, 479, 719, 863, 1153, 1213, 1283, 1307, 1523, 3467, 3733, 4007, 4621, 4787, 5087, 5113, 5413, 7523, 7703, 9817, 10333, 12347, 12539, 13381, 17027, 18553, 19717, 19813, 23399, 26003, 31873, 36097, 38833

Offset

1,1

Comments

Numbers n such that A257392(n) = 0.

Links

Robert Israel, Table of n, a(n) for n = 1..209

Example

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.

Maple

N:= 5000: # to get all terms <= N
Primes:= select(isprime, {2, seq(2*i+1, i=1..floor((N-1)/2))}):
Nonprimes:= sort(convert({$1..N} minus Primes, list)):
nnp:= nops(Nonprimes):
PSums:= [0, op(ListTools[PartialSums](Nonprimes))]:
A:= Primes:
mA:= max(A):
for i from 1 to nnp do
  for j from i+2 to nnp+1 while PSums[j] - PSums[i] <= mA do od;
  A:= A minus {seq(PSums[k]-PSums[i], k=i+2..j-1)};
od od:
A;
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(A, list));  # Robert Israel, Apr 21 2015

Mathematica

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 *)

Crossrefs

Cf. A257392, A018252, A141468.

Sequence in context: A206579 A349327 A166945 * A273814 A371131 A361988

Adjacent sequences: A257390 A257391 A257392 * A257394 A257395 A257396

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Apr 21 2015

Extensions

a(7) - a(26) from Michael De Vlieger, Apr 21 2015

a(27) - a(45) from Robert Israel, Apr 21 2015

Status

approved