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
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..209
Programs
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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 *)
Extensions
a(7) - a(26) from Michael De Vlieger, Apr 21 2015
a(27) - a(45) from Robert Israel, Apr 21 2015
Comments