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.

A231964 Lesser member of untouchable twin pairs, that is, such that a(n) and a(n)+2 are untouchable (A005114).

Original entry on oeis.org

246, 288, 290, 304, 322, 324, 406, 472, 516, 518, 624, 626, 668, 748, 766, 782, 802, 892, 894, 896, 934, 964, 1044, 1078, 1146, 1148, 1160, 1246, 1254, 1256, 1312, 1314, 1316, 1346, 1404, 1418, 1420, 1506, 1508, 1680, 1716, 1774, 1820, 1838, 1840, 1842, 1894
Offset: 1

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Author

Michel Marcus, Nov 16 2013

Keywords

Comments

There are 2673 terms in this sequence when the 8153 terms of A005114, up to 60000, are taken into account.
Note that some numbers come up by pairs like (288,290) or (322,324), corresponding to untouchable triples. Others come up by groups of 3 like (892,894,896) or (1312,1314,1316), corresponding to untouchable quadruplets. For higher n-tuplets, see A231965.

Examples

			246 and 248 are untouchable, so 246 is in this sequence.

Links

Crossrefs

Cf. A005114, A231965.

Programs

  • PARI
    lista() = {v = readvec("untouchable.log"); for (i=1, #v, vi = v[i]; if (vecsearch(v, vi+2, ), print1(vi, ", ")););} \\ Michel Marcus, Nov 16 2013

A110875 Minimum positive integer such that length of the gap described at A109322 is exactly n (in contrast to A109322 where the gap length is >= n).

Original entry on oeis.org

2, 16, 9, 64, 49, 872, 481, 1768, 423, 2980, 1333, 49180, 5335, 46666, 4425, 86815, 8763, 1109259, 14089, 658513, 29883, 137539, 22825, 10927365, 259843, 1667974, 46773, 7698572, 40291, 16048081, 178705, 16039804, 1135023, 132082042, 661285, 525395164
Offset: 1

Views

Author

Bojan Basic (bbasic(AT)ptt.yu), Sep 18 2005

Keywords

Comments

Conjectures and open problems: 1) It is not known whether the sequence is infinite; 2) It is conjectured that for every n there is corresponding a(n). If Conjecture 2) were proved, Conjecture 1) would follow as a direct consequence.
a(50) > 10^10. - Donovan Johnson, Jan 25 2012
Note that the sequence appears to undulate with terms that satisfy a(2n-1) < a(2n) < a(2n+1). Is there an explanation? - Michel Marcus, Nov 21 2013

Examples

			a(2)=16 because 16,17 are not contained in values of sigma(k) and 15,18 are; namely: sigma(8)=15 and sigma(10)=18, where sigma(k)=sum of all positive divisors of k.

Links

Crossrefs

Cf. A109322, A109323, A109324.
Cf. A231965 (analog for sigma(n) - n).

Programs

  • PARI
    oksuccs(v, vi, n) = {for (i = 1, n-1, if (! vecsearch(v, vi+i, ) , return (0));); return(! vecsearch(v, vi-1) && !vecsearch(v, vi+n));}
a(n) = {v = readvec("suntouch2.log"); for (i=1, #v, vi = v[i]; if (oksuccs(v, vi, n), return(vi)););} \\ where file read by readvec is the second column of b-file.  Michel Marcus, Nov 21 2013

A306747 Untouchable numbers with a record gap to the next untouchable number.

Original entry on oeis.org

2, 5, 2642, 546046
Offset: 1

Views

Author

Amiram Eldar, Mar 07 2019

Keywords

Comments

The record gap values are 3, 47, 62, 74.
Guy asks "How large can the gaps between untouchable numbers be?"

Examples

			5 is in the sequence since it is an untouchable number and the next untouchable number after it is 52 = 5 + 47 with a record gap of 47. The next gap which is larger than 47 occurs at 2642 which is followed by 2704 = 2642 + 62.

References

  • Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B10, p. 101.

Links

Crossrefs

Cf. A005114, A231965.
Showing 1-3 of 3 results.

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

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