A034111 Fractional part of square root of a(n) starts with 5: first term of runs.

21, 31, 43, 57, 73, 91, 111, 133, 157, 183, 211, 241, 273, 307, 343, 381, 421, 463, 507, 553, 601, 651, 703, 757, 813, 871, 931, 993, 1057, 1123, 1191, 1261, 1333, 1407, 1483, 1561, 1641, 1723, 1807, 1893, 1981, 2071, 2163, 2257, 2353, 2451, 2551, 2653

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base
• easy

Comments

Agrees with sequence A002061 (n^2-n+1 = central polygonal numbers) starting with sixth term.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A034101.

Programs

Mathematica

Array[#^2 + 7 # + 13 &, 48] (* Michael De Vlieger, Aug 05 2020 *)
LinearRecurrence[{3,-3,1},{21,31,43},50] (* Harvey P. Dale, Apr 29 2022 *)

PARI

a(n)=n^2+7*n+13 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = n^2 + 7*n + 13. - Charles R Greathouse IV, Aug 10 2010

Extensions

Offset 1 from Alois P. Heinz, Aug 05 2020