A371100
Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(n, k) = 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3, n,k >= 1.
Original entry on oeis.org
21, 21, 45, 341, 117, 69, 341, 725, 213, 93, 5461, 1877, 1109, 309, 117, 5461, 11605, 3413, 1493, 405, 141, 87381, 30037, 17749, 4949, 1877, 501, 165, 87381, 185685, 54613, 23893, 6485, 2261, 597, 189, 1398101, 480597, 283989, 79189, 30037, 8021, 2645, 693, 213, 1398101, 2970965, 873813, 382293, 103765, 36181, 9557, 3029, 789, 237
Offset: 1
The top left corner of the array:
n\k| 1 2 3 4 5 6 7 8
---+--------------------------------------------------------------------------
1 | 21, 45, 69, 93, 117, 141, 165, 189, ...
2 | 21, 117, 213, 309, 405, 501, 597, 693, ...
3 | 341, 725, 1109, 1493, 1877, 2261, 2645, 3029, ...
4 | 341, 1877, 3413, 4949, 6485, 8021, 9557, 11093, ...
5 | 5461, 11605, 17749, 23893, 30037, 36181, 42325, 48469, ...
6 | 5461, 30037, 54613, 79189, 103765, 128341, 152917, 177493, ...
7 | 87381, 185685, 283989, 382293, 480597, 578901, 677205, 775509, ...
8 | 87381, 480597, 873813, 1267029, 1660245, 2053461, 2446677, 2839893, ...
...
Cf.
A372351 (same terms, in different order),
A372290 (sorted into ascending order, without duplicates),
A372293 (odd numbers that do not occur here).
Leftmost column is
A144864 duplicated, without its initial 1.
-
A371100[n_, k_] := 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3;
Table[A371100[n - k + 1, k], {n, 10}, {k, n}] (* Paolo Xausa, Apr 21 2024 *)
-
up_to = 55;
A371100sq(n,k) = 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3;
A371100list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A371100sq((a-(col-1)),col))); (v); };
v371100 = A371100list(up_to);
A371100(n) = v371100[n];
A371102
Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(1, k) = 4*k-1, and A(n+1, k) = A371094(A(n, k)), n,k >= 1.
Original entry on oeis.org
3, 21, 7, 5461, 45, 11, 357913941, 1109, 69, 15, 1537228672809129301, 873813, 3413, 93, 19, 28356863910078205288614550619314017621, 1466015503701, 22369621, 2261, 117, 23, 9649340769776349618630915417390658987772498722136713669954798667326094136661, 25790417485112089060398421, 6004799503160661, 873813, 11605, 141, 27
Offset: 1
Array begins:
n\k| 1 2 3 4 5 6 7
---+--------------------------------------------------------------------
1 | 3, 7, 11, 15, 19, 23, 27,
2 | 21, 45, 69, 93, 117, 141, 165,
3 | 5461, 1109, 3413, 2261, 11605, 3413, 8021,
4 | 357913941, 873813, 22369621, 873813, 72701269, 22369621, 12408149,
-
up_to = 105;
A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
A371102sq(n,k) = if(1==n,4*k-1,A371094(A371102sq(n-1,k)));
A371102list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A371102sq((a-(col-1)),col))); (v); };
v371102 = A371102list(up_to);
A371102(n) = v371102[n];
A372290
Numbers that occur in the odd bisection of A371094.
Original entry on oeis.org
21, 45, 69, 93, 117, 141, 165, 189, 213, 237, 261, 285, 309, 333, 341, 357, 381, 405, 429, 453, 477, 501, 525, 549, 573, 597, 621, 645, 669, 693, 717, 725, 741, 765, 789, 813, 837, 861, 885, 909, 933, 957, 981, 1005, 1029, 1053, 1077, 1101, 1109, 1125, 1149, 1173, 1197, 1221, 1245, 1269, 1293, 1317, 1341, 1365, 1389
Offset: 1
21 is present because A371094(1) = A371094(3) = 21.
45 is present because A371094(7) = 45.
87381 is present because A371094(85) = A371094(213) = A371094(7281) = A371094(14563) = 87381.
-
A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
isA372290(n) = if(!(n%2),0,forstep(k=1,n,2,if(A371094(k)==n,return(1))); (0));
-
A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
A372290list(up_to_n) = { my(v=vector((1+up_to_n)/2), x, lista=List([])); forstep(k=1,up_to_n,2,x=A371094(k); if(x <= up_to_n, v[(x+1)/2]++)); for(i=1,(1+up_to_n)/2,if(v[i]>0, listput(lista,i+i-1))); Vec(lista); };
Showing 1-3 of 3 results.
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