A108770 Numbers k such that k^2 + (k+1)^2 is a brilliant number.

3, 10, 15, 20, 27, 37, 59, 92, 105, 120, 152, 155, 175, 190, 215, 219, 242, 245, 254, 255, 277, 300, 302, 307, 325, 337, 362, 365, 370, 402, 415, 614, 930, 944, 987, 1049, 1059, 1112, 1192, 1204, 1210, 1220, 1265, 1312, 1344, 1360, 1374, 1449, 1460, 1504, 1527

Offset

1,1

Comments

Consecutive terms are (254,255) (4099,4100) (11159,11160) (25094,25095) (31754,31755) (40189,40190) ... Conjecture: There are infinitely many consecutive values.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

92 is a term because 92^2 + 93^2 = 17113 = 109*157 and both of its
factors have three digits.

Mathematica

Select[Range[1600], With[{f=Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[#^2+(#+1)^2]]}, Length[f]==2&&IntegerLength[f[[1]]]==IntegerLength[f[[2]]]]&] (* Harvey P. Dale, May 17 2026 *)

Crossrefs

Cf. A078972, A027861.

Sequence in context: A134102 A173600 A328987 * A112355 A074314 A077759

Adjacent sequences: A108767 A108768 A108769 * A108771 A108772 A108773

Keyword

base,easy,nonn

Author

Jason Earls, Jun 25 2005

Status

approved