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.

A169595 Primes p such that sigma(p+2)=sigma(p-2).

Original entry on oeis.org

53, 20543, 47843, 176227, 396953, 471187, 995887, 1083113, 1867253, 5022653, 17449567, 22873583, 32003407, 38673847, 59808803, 96144127, 113561243, 143570873, 164563687, 225835807, 238818893, 272773499, 286557983, 349504957
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 03 2009

Keywords

Links

Crossrefs

Cf. A067891.
Subsequence of A223091.

Programs

  • Mathematica
    f[n_]:=Plus@@Divisors[Prime[n]-2]==Plus@@Divisors[Prime[n]+2]; lst={};Do[If[f[n],AppendTo[lst,Prime[n]]],{n,2*9!}];lst

Extensions

a(11)-a(24) from Donovan Johnson, Dec 08 2009
a(25)-a(200) from Martin Møller Skarbiniks Pedersen, May 31 2016

A217768 Smallest number k > 0 for which sigma(k - n) = sigma(k + n).

Original entry on oeis.org

34, 53, 23, 19, 26, 41, 31, 38, 49, 52, 68, 82, 112, 80, 103, 76, 110, 123, 4, 83, 101, 136, 3, 164, 130, 5, 147, 133, 381, 254, 7, 149, 253, 1, 131, 246, 172, 8, 404, 7, 6, 312, 148, 209, 309, 241, 487, 328, 9, 260
Offset: 1

Views

Author

Jayanta Basu, Mar 24 2013

Keywords

Comments

The sigma() in the definition is the sum-of-divisors function A000203.
If m is negative, the definition uses the convention sigma(m) = sigma(-m).

Examples

			a(4) = 19 because sigma(19 + 4) = sigma(23) = 1 + 23 = 24 and sigma(19 - 4) = sigma(15) = 1 + 3 + 5 + 15 = 24 and there is no k < 19 for which sigma(k + 4) = sigma(k - 4).
a(26) = 5 because sigma(5 + 26) = sigma(31) = 1 + 31 = 32 and sigma(5 - 26) = sigma(-21) = sigma(21) = 1 + 3 + 7 + 21 = 32.

Crossrefs

Cf. A067135, A175876, A223091.

Programs

  • Mathematica
    Table[Min[Select[Range[500],DivisorSigma[1, # - n] == DivisorSigma[1, # + n] &]], {n,50}]

A218466 Least k > n for which phi(k - n) = phi(k + n) or 0 if no such k exists.

Original entry on oeis.org

5, 10, 27, 17, 25, 54, 23, 34, 61, 47, 55, 108, 47, 46, 139, 68, 58, 122, 71, 85, 144, 95, 115, 207, 101, 94, 183, 92, 145, 278, 104, 136, 177, 116, 175, 244, 161, 142, 306, 149, 184, 283, 191, 187, 410, 230, 235, 267, 146, 202, 299, 188, 157, 366, 275, 184
Offset: 1

Views

Author

Irina Gerasimova, Mar 26 2013

Keywords

Comments

Is there an upper bound for a(n) for a given n? - Michael B. Porter, Apr 06 2013

Examples

			a(3) = 27 since phi(27 - 3) = phi(24) = 8 and phi(27 + 3) = phi(30) = 8, and 27 is the smallest number greater than 3 for which the two are equal.

Links

Crossrefs

Cf. A000010, A217768, A223091.

Programs

  • PARI
    /* will not terminate if k does not exist */
a218446(n) = {local(k); k = n + 1; while(eulerphi(k - n) <> eulerphi(k + n), k = k + 1); k} \\ Michael B. Porter, Mar 30 2013

Extensions

Extended by R. J. Mathar, Mar 27 2013
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.