Original entry on oeis.org
1, 2, 3, 4, 5, 7, 32, 52, 55, 61, 128, 194, 214, 244, 292, 334, 388, 782, 902, 992, 1414, 1571, 1712, 1916, 2551
Offset: 1
A276520(1,2,3,4,5)=0, so a(1)=1, a(2)=2, a(3)=3, a(4)=4, and a(5)=5.
The next zero: A276520(7)=0, so a(6)=7.
-
p = 3; sp = {p}; m = 0; Table[While[m++; l = Length[sp]; While[sp[[l]] < m, While[p = NextPrime[p]; cp = 2*3^(Floor[Log[3, 2*p - 1]]) - p; ! PrimeQ[cp]]; AppendTo[sp, p]; l++]; c = 2 - Mod[m + 1, 2]; ct = 0; Do[If[MemberQ[sp, m - c*sp[[i]]], If[c == 1, If[(2*sp[[i]]) <= m, ct++], ct++]], {i, 1, l}]; ct != 0]; m, {n, 1, 25}]
A278341
a(n) is the number of decompositions of n into unordered form p + c*q, where p, q are terms of A274987 and the difference of trits for p and q is no more than 1, c=1 for even n-s and c=2 for odd n-s.
Original entry on oeis.org
0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 2, 1, 2, 2, 1, 2, 2, 1, 3, 2, 2, 2, 2, 0, 3, 2, 1, 2, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 1, 1, 3, 0, 2, 2, 0, 0, 3, 0, 2, 1, 0, 1, 2, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 2, 1, 1, 2, 0, 1, 1, 1, 2, 2, 0, 2
Offset: 1
A274987 = {3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 59, 61, 73, 79, 83, 89, 101, 103, 109...}
For n=6, c=1, 6=3+3, 3=10 in balanced ternary(BT). 3 is a 2 trits BT number. 2-2=0<1, so this one counts, a(6)=1;
...
For n=20, c=1, 20=3+17=7+13. For 3 and 17 pair, 3=10(BT), 17=1T0T(BT), the difference of trits of these two primes is 2. This does not count. For 7 and 13 pair, 7=1T1(BT), 13=111(BT), the difference of trits of these two primes is 0. This is counted. So a(20)=1;
...
For n=29, c=2, 29=23+2*3=7+2*11=3+2*13. For 23 and 3 pair, 23=10TT(BT), 3=10(BT), the difference of trits of these two primes is 2, this does not count; for 7 and 11 pair, 7=1T1(BT), 11=11T(BT), the difference of trits of these two primes is , this is counted; for 3 and 13 pair, 3=10(BT), 13=111(BT), the difference of trits of these two primes is 1, this is counted. So a(29)=2.
-
p = 3; sp = {p}; Table[l = Length[sp]; While[sp[[l]] < n, While[p = NextPrime[p]; cp = 2*3^(Floor[Log[3, 2*p - 1]]) - p; ! PrimeQ[cp]]; AppendTo[sp, p]; l++]; c = 2 - Mod[n + 1, 2]; ct = 0; Do[If[MemberQ[sp, n - c*sp[[i]]], If[Abs[Floor[Log[3, 2*sp[[i]] - 1]] - Floor[Log[3, 2*(n - c*sp[[i]]) - 1]]] <= 1, If[c == 1, If[(2*sp[[i]]) <= n, ct++], ct++]]], {i, 1, l}];
ct, {n, 1, 87}]
Showing 1-2 of 2 results.
Comments