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A257393 Primes which are not the sum of two or more consecutive nonprime numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A007996 A206579 A166945 * A273814 A085872 A070858

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

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Last modified June 25 23:52 EDT 2019. Contains 324367 sequences. (Running on oeis4.)