OFFSET
1,2
COMMENTS
A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are numbers whose distinct prime indices have no binary carries.
EXAMPLE
Most small numbers are in the sequence, however the sequence of non-terms together with their prime indices begins:
10: {1,3}
15: {2,3}
20: {1,1,3}
22: {1,5}
30: {1,2,3}
34: {1,7}
39: {2,6}
40: {1,1,1,3}
44: {1,1,5}
45: {2,2,3}
46: {1,9}
50: {1,3,3}
51: {2,7}
55: {3,5}
60: {1,1,2,3}
62: {1,11}
65: {3,6}
66: {1,2,5}
68: {1,1,7}
70: {1,3,4}
MATHEMATICA
binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Select[Range[100], stableQ[PrimePi/@First/@FactorInteger[#], Intersection[binpos[#1], binpos[#2]]!={}&]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 27 2019
STATUS
approved