A226383 Odd numbers >1 for which there is at least one 3-smooth representation that is special of level k, including repeats if there are multiple representations.

5, 7, 11, 19, 19, 23, 29, 31, 35, 37, 47, 49, 53, 65, 65, 67, 73, 79, 85, 85, 89, 89, 97, 101, 103, 119, 121, 121, 125, 131, 133, 143, 143, 149, 151, 157, 161, 169, 175, 179, 185, 185, 197, 205, 211, 211, 215, 221, 223, 227, 233, 239, 251, 259, 259, 259, 269, 271, 275, 277, 283, 287, 287, 289, 313, 313, 319, 323, 323

Offset

1,1

Comments

These numbers are of the form 3^k*2^0 + 3^{k-1}*2^{a_1} + ... + 3^1*2^{a_{k-1}} + 3^0*2^{a_k} in which every power 3^i appears, 0 <= i <= k, and where a_i satisfies a_0 = 0, a_0 < a_1 < ... < a_k.

References

Kenneth Vollmar, Recursive calculation of 3-smooth representations special of level k, To be submitted mid-2013.

Links

Thomas Scheuerle, Table of n, a(n) for n = 1..5000

Richard Blecksmith, Michael McCallum and J. L. Selfridge, 3-smooth representations of integers, Amer. Math. Monthly, 105 (1998), 529-543.

Prog

(PARI) A348175(n, k) = my(ret=0); for(i=0, n-1, if(bittest(k, n-1-i), ret=3*ret+1<<i)); ret;
listA(up_to) = {my(maxexp=if( up_to<2, 0, exponent(up_to-1)+1), v=[], temp=0); for(ex=0, maxexp, for(k=0, 2^ex-1, temp=A348175(ex+1, 2*k+1); if(temp<=up_to && temp>1 && temp%2==1, v=concat(v, temp)))); vecsort(v)} \\ Thomas Scheuerle, Oct 01 2025

Crossrefs

Cf. A213539 (Even and odd terms).

Cf. A116641 (Without repeats and including 1).

Cf. A003586.

Sequence in context: A394631 A280651 A089785 * A118386 A240849 A116641

Adjacent sequences: A226380 A226381 A226382 * A226384 A226385 A226386

Keyword

nonn

Author

Kenneth Vollmar, Jun 05 2013

Extensions

Name and offset changed by Thomas Scheuerle, Oct 01 2025

Status

approved