A227321 -id:A227321 - cp's OEIS frontend

A228003 Places of records of A227321.

0, 4, 11, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 211, 223, 229, 241, 271, 283, 313, 349, 379, 409, 421, 433, 439, 463, 523, 571, 601, 613, 619, 631, 643, 649

Offset: 1

Vladimir Shevelev, Aug 07 2013

nonn

Records of A227321 are 3, 4, 5, 8, 11, 17, 23, 32, 38,....
The first 3 nonprimes are a(1)=0, a(2)=4, a(38)=649.
The sequence contains all greaters of twin primes more than 7 (see A006512).

Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Cf. A227321, A006512.

For n>=4, A227321(a(n)) = (a(n) + 3)/2.

More terms from Peter J. C. Moses, Aug 07 2013

A227727 a(n) is the least r>=3 such that the difference between n and the nearest r-gonal number<=n is an r-gonal number.

Original entry on oeis.org

3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 5, 3, 7, 3, 3, 4, 3, 7, 4, 3, 3, 5, 3, 4, 4, 3, 3, 3, 11, 3, 16, 9, 3, 5, 3, 3, 19, 3, 4, 7, 3, 6, 22, 3, 3, 5, 3, 4, 4, 3, 5, 4, 19, 3, 3, 15, 3, 11, 6, 3, 7, 5, 4, 3, 3, 3, 4, 3, 5, 5, 3, 4, 37, 5, 3, 14, 3, 3, 4, 3, 4, 13

Offset: 0

Vladimir Shevelev, Jul 30 2013

nonn

The n-th r-gonal number is n((n-1)r-2(n-2))/2, such that 3-gonal numbers are triangular numbers, 4-gonal numbers are squares, etc.

Peter J. C. Moses, Table of n, a(n) for n = 0..1999

Cf. A227321.

rGonalQ[r_,0]:=True; rGonalQ[r_,n_]:=IntegerQ[(Sqrt[((8r-16)n+(r-4)^2)]+r-4)/(2r-4)]; nthrGonal[r_,n_]:=(n (r-2)(n-1))/2+n; prevrGonal[r_,n_]:=nthrGonal[r,Floor[(Sqrt[((8r-16)n+(r-4)^2)]+r-4)/(2r-4)]]; (* previous r-gonal number greater than or equal to n *) Table[NestWhile[#+1&,3,!rGonalQ[#,n-prevrGonal[#,n]]&],{n,0,99}] (* Peter J. C. Moses, Aug 03 2013 *)

More terms from Peter J. C. Moses, Jul 30 2013

cp's OEIS Frontend

A228003 Places of records of A227321.

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