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 1-5 of 5 results.

A277908 Numbers n for which abs(n-A277911(n)) = 1.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 14, 15, 20, 21, 23, 24, 33, 34, 35, 36, 37, 38, 43, 44, 46, 47, 50, 51, 60, 61, 64, 65, 66, 67, 76, 77, 90, 91, 93, 94, 103, 104, 105, 106, 116, 117, 127, 128, 140, 141, 144, 145, 147, 148, 154, 155, 163, 164, 167, 168, 200, 201, 206, 207, 215, 216, 247, 248, 275, 276, 285, 286, 287, 288, 293, 294, 295, 296, 303, 304, 313, 314
Offset: 1

Views

Author

Antti Karttunen, Nov 05 2016

Keywords

Links

Crossrefs

Cf. A007310, A277907, A277911.
Bisections: A277909, A277910.

Formula

A007310(a(n)) = A277907(n).

A277909 Numbers n for which A277911(n) = n+1.

Original entry on oeis.org

2, 4, 6, 14, 20, 23, 33, 35, 37, 43, 46, 50, 60, 64, 66, 76, 90, 93, 103, 105, 116, 127, 140, 144, 147, 154, 163, 167, 200, 206, 215, 247, 275, 285, 287, 293, 295, 303, 313, 323, 337, 340, 344, 363, 365, 410, 427, 430, 433, 435, 440, 476, 483, 495, 497, 523, 527, 533, 536, 555, 566, 596, 623, 625, 665, 667, 676, 694, 696, 714, 747, 757
Offset: 1

Views

Author

Antti Karttunen, Nov 05 2016

Keywords

Links

Crossrefs

Odd bisection of A277908.
One less than A277910.
Cf. A277911.

A277910 Numbers n for which A277911(n) = n-1.

Original entry on oeis.org

3, 5, 7, 15, 21, 24, 34, 36, 38, 44, 47, 51, 61, 65, 67, 77, 91, 94, 104, 106, 117, 128, 141, 145, 148, 155, 164, 168, 201, 207, 216, 248, 276, 286, 288, 294, 296, 304, 314, 324, 338, 341, 345, 364, 366, 411, 428, 431, 434, 436, 441, 477, 484, 496, 498, 524, 528, 534, 537, 556, 567, 597, 624, 626, 666, 668, 677, 695, 697, 715, 748, 758
Offset: 1

Views

Author

Antti Karttunen, Nov 05 2016

Keywords

Links

Crossrefs

Even bisection of A277908.
One more than A277909.
Cf. A277911.

Formula

a(n) = 1 + A277909(n).

A118306 If n = product{k>=1} p(k)^b(n,k), where p(k) is the k-th prime and where each b(n,k) is a nonnegative integer, then: If n occurs earlier in the sequence, then a(n) = product{k>=2} p(k-1)^b(n,k); If n does not occur earlier in the sequence, then a(n) = product{k>=1} p(k+1)^b(n,k).

Original entry on oeis.org

1, 3, 2, 9, 7, 15, 5, 27, 4, 21, 13, 45, 11, 33, 6, 81, 19, 75, 17, 63, 10, 39, 29, 135, 49, 51, 8, 99, 23, 105, 37, 243, 14, 57, 77, 225, 31, 69, 22, 189, 43, 165, 41, 117, 12, 87, 53, 405, 25, 147, 26, 153, 47, 375, 91, 297, 34, 93, 61, 315, 59, 111, 20, 729, 119, 195, 71
Offset: 1

Views

Author

Leroy Quet, May 14 2006

Keywords

Comments

Sequence is a permutation of the positive integers and it is its own inverse permutation.
From Antti Karttunen, Nov 05 2016: (Start)
A016945 gives the positions of even terms.
A007310 is closed with respect to this permutation. See A277911 for the permutation induced.
A029744 (without 3) seems to give the positions of records in this sequence (note that it gives the record positions in related A003961 and A048673) which implies that A083658 (without its term 5) would then give the record values.
(End)

Links

Crossrefs

Cf. A003961, A064989, A007310, A016945, A029744, A048673, A055396, A083221, A083658, A246277, A246278, A249734, A277911.

Programs

  • Maple
    A064989 := proc(n) local a,ifs,p ; a := 1 ; ifs := ifactors(n)[2] ; for p in ifs do if op(1,p) > 2 then a := a* prevprime(op(1,p))^op(2,p) ; fi ; od; RETURN(a) ; end: A003961 := proc(n) local a,ifs,p ; a := 1 ; ifs := ifactors(n)[2] ; for p in ifs do a := a* nextprime(op(1,p))^op(2,p) ; od; RETURN(a) ; end: A118306 := proc(nmin) local a,anxt,i,n ; a := [1] ; while nops(a) < nmin do n := nops(a)+1 ; if n in a then anxt := A064989(n) ; else anxt := A003961(n) ; fi ; a := [op(a),anxt] ; od; a ; end: A118306(100) ; # R. J. Mathar, Sep 06 2007
  • PARI
    A118306(n) = { if(1==n, 1, my(f = factor(n)); my(d = (-1)^primepi(f[1, 1])); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-d)); factorback(f)); }; \\ Antti Karttunen, Nov 06 2016
for(n=1, 10001, write("b118306.txt", n, " ", A118306(n)));
  • Scheme
    (define (A118306 n) (cond ((= 1 n) n) ((odd? (A055396 n)) (A003961 n)) (else (A064989 n)))) ;; Antti Karttunen, Nov 05 2016

Formula

From Antti Karttunen, Nov 05 2016: (Start)
a(1) = 1; and for n > 1, if n = a(k) for some k = 1 .. n-1, then a(n) = A064989(n), otherwise a(n) = A003961(n). [After the original definition and R. J. Mathar's Maple-code]
a(1) = 1, and for n > 1, if A055396(n) is odd, a(n) = A003961(n), otherwise a(n) = A064989(n). [The above reduces to this.]
a(n) = product{k>=1} prime(k-((-1)^A055396(n)))^e(k) when n = product{k>=1} prime(k)^e(k).
a(2n) = A249734(n) and a(A249734(n)) = 2n.
A126760(a(A007310(n))) = A277911(n).
For n > 1, A055396(a(n)) = A055396(n) - (-1)^A055396(n). [Permutation sends the terms on any odd row of A246278 to the next even row just below, and vice versa.]
A246277(a(n)) = A246277(n). [While keeping them in the same column.]
a(n) = A064989(A064989(a(A003961(A003961(n))))).
(End)

Extensions

More terms from R. J. Mathar, Sep 06 2007
A small omission in the definition corrected by Antti Karttunen, Nov 05 2016

A277907 a(n) = A007310(A277908(n)).

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 41, 43, 59, 61, 67, 71, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 179, 181, 191, 193, 197, 199, 227, 229, 269, 271, 277, 281, 307, 311, 313, 317, 347, 349, 379, 383, 419, 421, 431, 433, 439, 443, 461, 463, 487, 491, 499, 503, 599, 601, 617, 619, 643, 647, 739, 743, 823, 827, 853, 857, 859, 863, 877, 881
Offset: 1

Views

Author

Antti Karttunen, Nov 05 2016

Keywords

Comments

It seems that all terms are primes, and moreover, that all those primes occur in pairs with distance of 2 or 4. However, not all terms of A001359 are present.

Links

Crossrefs

Cf. A000040, A001359, A007310, A118306, A277908, A277911.

Programs

Formula

a(n) = A007310(A277908(n)).
Showing 1-5 of 5 results.

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