A081310 Numbers having no representation as sum of a prime and an 3-smooth number.

1, 2, 36, 78, 96, 120, 126, 144, 156, 162, 186, 204, 210, 216, 222, 276, 288, 300, 306, 324, 328, 330, 336, 342, 366, 372, 378, 396, 408, 414, 426, 438, 456, 474, 486, 498, 516, 528, 534, 540, 546, 552, 562, 576, 582, 606, 612, 624, 630, 636, 666, 672, 690

Offset

1,2

Comments

Complement of A081311.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A081308(a(n)) = 0.

Example

For all primes p<36 the greatest prime factor of 36-p is >3: 36-2=2*17, 36-3=3*11, 36-5=31, 36-7=29, 36-11=5*5, 36-13=23, 36-17=19, 36-19=17, 36-23=13, 36-29=7, 36-31=5, therefore 36 is a term.

Mathematica

nmax = 1000;
S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
A081308[n_] := Count[TakeWhile[S, # < n &], s_ /; PrimeQ[n - s]];
Select[Range[nmax], A081308[#] == 0 &] (* Jean-François Alcover, Oct 13 2021 *)

Prog

(Haskell)
a081310 n = a081310_list !! (n-1)
a081310_list = filter ((== 0) . a081308) [1..]
-- Reinhard Zumkeller, Jul 04 2012

Crossrefs

Cf. A000040, A003586, A081308, A081311.

Sequence in context: A239343 A058517 A328963 * A187298 A069067 A278930

Adjacent sequences: A081307 A081308 A081309 * A081311 A081312 A081313

Keyword

nonn

Author

Reinhard Zumkeller, Mar 17 2003

Status

approved