The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by M. F. Hasler

(See also M. F. Hasler's wiki page
and changes approved by M. F. Hasler)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A155712

Intersection of A092572 and A155716: N = a^2 + 3b^2 = c^2 + 6d^2 for some positive integers a,b,c,d.
(history; published version)

#6 by M. F. Hasler at Sat Jan 18 20:58:36 EST 2025

STATUS

editing

proposed

#5 by M. F. Hasler at Sat Jan 18 20:58:25 EST 2025

PROG

(PARI) isA155712(n, /* optional 2nd arg allows us to get other sequences */c=[6, 3]) = { for(i=1, #c, for(b=1, sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & & next(2)); return); 1}

for( n=1, 999, isA155712(n) & & print1(n", ")) \\ Update to modern PARI syntax (& -> &&) by _M. F. Hasler_, Jan 18 2025

STATUS

approved

editing

A377091

a(0) = 0; thereafter a(n) is the least integer (in absolute value) not yet in the sequence such that the absolute difference of a(n-1) and a(n) is a square; in case of a tie, preference is given to the positive value.
(history; published version)

#93 by M. F. Hasler at Sat Jan 18 20:42:53 EST 2025

STATUS

editing

proposed

Discussion

Sat Jan 18

20:47

M. F. Hasler: (Again the .txt extension appended to the file name by the server must be removed. Note that the old version was also renamed to ..._2.html.)

20:53

M. F. Hasler: Instead of "within X of Y", maybe  "within Y +-  X" would be easier to understand...?
Conjecture 1 is certainly true.
But isn't the conjecture 2 wrong for n=2? a(n)=2 is not within sqrt(2)/2 = 0.7 of floor(n/2) = 1. Or am I missing something?

#92 by M. F. Hasler at Sat Jan 18 20:41:16 EST 2025

PROG

(PARI) A377091_upto(n, S=[])={vector(n+1, k, S=setunion(S, [n=if(k>1, k=1; while(setsearch(S, k) || !issquare(abs(n-k)), k=(k<0)-k); k)]); n)} \\ M. F. Hasler, Jan 18 2025

Discussion

Sat Jan 18

20:42

M. F. Hasler: New version of the "interactive illustration" with several colouring and other formatting options.

#91 by M. F. Hasler at Sat Jan 18 20:25:53 EST 2025

LINKS

M. F. Hasler, <a href="/A377091/a377091_2.html">Interactive spiral graph representation of the first n terms</a>, Jan 18 2025

M. F. Hasler, <a href="/A377091/a377091_2.html.txt">Interactive spiral graph representation of the first n terms</a>, Jan 18 2025

STATUS

approved

editing

#63 by M. F. Hasler at Sat Jan 18 15:46:06 EST 2025

STATUS

editing

proposed

#62 by M. F. Hasler at Sat Jan 18 15:45:14 EST 2025

LINKS

M. F. Hasler, <a href="/A377091/a377091_12.html.txt">Interactive Spiral graph representation of the first n terms</a>, Jan 18 2025

Discussion

Sat Jan 18

15:46

M. F. Hasler: Another minor change (vertically flipped so that it's the same as Neil's drawing).

#61 by M. F. Hasler at Sat Jan 18 15:37:17 EST 2025

LINKS

M. F. Hasler, <a href="/A377091/a377091_1.html.txt">Interactive Spiral graph representation of the first n terms</a>, Jan 18 2025

STATUS

proposed

editing

#60 by M. F. Hasler at Sat Jan 18 15:34:36 EST 2025

STATUS

editing

proposed

#59 by M. F. Hasler at Sat Jan 18 15:32:38 EST 2025

LINKS

M. F. Hasler, <a href="/A377091/a377091.html.txt">Interactive Spiral graph representation of the first n terms</a>, Jan 18 2025

STATUS

approved

editing

Discussion

Sat Jan 18

15:34

M. F. Hasler: The file (and link) must be renamed to xxx.html (i.e., the added ".txt" must be removed) for this to work. - Thanks!