The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A144923 Triangle read by rows: |A144912(b, b^2 + k)| if it is prime and 0 otherwise, with rows b in {2, 4, 6, ...} and columns k in {0, 1, 3, 4, 6, 7, ..., b}. 1
 0, 0, 7, 5, 0, 5, 13, 11, 7, 5, 11, 19, 17, 13, 11, 7, 5, 0, 23, 19, 17, 13, 11, 7, 23, 31, 29, 0, 23, 19, 17, 13, 11, 29, 37, 0, 31, 29, 0, 23, 19, 17, 13, 11, 43, 41, 37, 0, 31, 29, 0, 23, 19, 17, 13, 41, 0, 47, 43, 41, 37, 0, 31, 29, 0, 23, 19, 17, 47 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS This triangle is roughly twice the usual width. Odd rows and columns congruent to 2 modulo 3 are omitted; otherwise the triangle would begin like this: 2:..0...0...0 3:..0...2...0...2 4:..7...5...3...0...5 5:..0...0...0...0...2...0 6:.13..11...0...7...5...3..11 7:..0...0...0...0...0...0...0...0 8:.19..17...0..13..11...0...7...5..17 Every odd row afterward would then be entirely filled with zeros and every third column would contain zeros, often following an initial prime. The triangle begins as follows: b --+b^2..+0..+1..+3..+4..+6..+7..+9.+10.+12 2.:......0...0 4.:......7...5...0...5 6.:.....13..11...7...5..11 8.:.....19..17..13..11...7...5 10:......0..23..19..17..13..11...7..23 12:.....31..29...0..23..19..17..13..11..29 Some diagonals are entirely filled with zeros; for example, the first such diagonal begins at b = 32 and there is another for b in [40, 42]. The fraction |A144912(b, b^2)| / b approaches 3 or nearly 3. For n = b and m = b + 2, ((n, x) + (m, x)) / 2 approximates (m, x + 1) = (n, x - 1), where x is the index of a column disregarding k. The units digit in columns follows the repeating sequence {1, 7, 3, 9, 5}, with nearly all fives omitted and occasional other omissions. The units digit in rows follows the sequence {1, 9, 5, 3, 9, 7, 3, 1, 7, 5}. The complete repeating unit is: 1 9 5 3 9 7 3 1 7 5 7 5 1 9 5 3 9 7 3 1 3 1 7 5 1 9 5 3 9 7 9 7 3 1 7 5 1 9 5 3 5 3 9 7 3 1 7 5 1 9 LINKS PROG (PARI) T(b, k) = {my(d=digits(k, b)); if(isprime(d=abs(sum(i=1, #d, 2*d[i]-b+1))), d, 0); } row(n) = {my(v=[]); for(k=0, 2*n, if(k%3<2, v=concat(v, T(2*n, 4*n^2+k)))); v; } \\ Jinyuan Wang, Jul 21 2020 CROSSREFS Cf. A144912, A145009. Sequence in context: A241902 A113223 A096414 * A184908 A197519 A290374 Adjacent sequences:  A144920 A144921 A144922 * A144924 A144925 A144926 KEYWORD nonn,base,easy,tabf AUTHOR Reikku Kulon, Sep 25 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 30 20:55 EST 2020. Contains 338812 sequences. (Running on oeis4.)