cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Antti Karttunen, Apr 26 2024

Keywords

Comments

Numbers that occur in array A371100.

Examples

			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.
		

Crossrefs

Union of A372291 and A372292.
Cf. A102603 (subsequence), A371094, A371100.

Programs

  • PARI
    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));
    
  • PARI
    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); };

A372351 Odd bisection of A371094.

Original entry on oeis.org

21, 21, 341, 45, 117, 69, 341, 93, 213, 117, 5461, 141, 309, 165, 725, 189, 405, 213, 1877, 237, 501, 261, 1109, 285, 597, 309, 5461, 333, 693, 357, 1493, 381, 789, 405, 3413, 429, 885, 453, 1877, 477, 981, 501, 87381, 525, 1077, 549, 2261, 573, 1173, 597, 4949, 621, 1269, 645, 2645, 669, 1365, 693, 11605, 717
Offset: 1

Views

Author

Antti Karttunen, Apr 28 2024

Keywords

Crossrefs

Row 2 of A372282.
Cf. A371094, and array A371100 (gives the same terms, in different order).
Cf. A372290 (the range of this sequence), A372291 (numbers that occur only once), A372292 (more than once), A372293 (odd numbers not occurring here).

Programs

  • Mathematica
    Table[With[{e = IntegerExponent[6*n - 2, 2]}, (6*n - 2)*2^e + (4^e - 1)/3], {n, 100}] (* Paolo Xausa, Apr 29 2024 *)
  • PARI
    A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
    A372351(n) = A371094(n+n-1);
    
  • Python
    def A372351(n): return ((m:=6*n-2)<<(e:=(~m & m-1).bit_length()))+((1<<(e<<1))-1)//3 # Chai Wah Wu, Apr 28 2024

Formula

a(n) = A371094(2*n-1).

A372291 Numbers that occur exactly once in the odd bisection of A371094.

Original entry on oeis.org

45, 69, 93, 141, 165, 189, 237, 261, 285, 333, 357, 381, 429, 453, 477, 525, 549, 573, 621, 645, 669, 717, 725, 741, 765, 813, 837, 861, 909, 933, 957, 1005, 1029, 1053, 1101, 1109, 1125, 1149, 1197, 1221, 1245, 1293, 1317, 1341, 1389, 1413, 1437, 1485, 1493, 1509, 1533, 1581, 1605, 1629, 1677, 1701, 1725, 1773, 1797
Offset: 1

Views

Author

Antti Karttunen, Apr 26 2024

Keywords

Comments

Numbers that occur exactly once in array A371100.

Examples

			45 is present because A371094(k) = 45 for no other odd number than k=7.
		

Crossrefs

Setwise difference A372290 \ A372292.

Programs

  • PARI
    A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
    isA372291(n) = if(!(n%2),0,my(c=0); forstep(k=1,n,2,if(A371094(k)==n,c++;if(c>1,return(0)))); (c));
Showing 1-3 of 3 results.