A368416 Numbers k whose decimal expansion can be split into two parts s and t with k = s^2 + t^2.
101, 1233, 8833, 10100, 990100, 5882353, 94122353, 1765038125, 2584043776, 7416043776, 8235038125, 116788321168, 123288328768, 876712328768, 883212321168, 7681802663025, 8896802846976, 13793103448276, 15348303604525, 84651703604525, 86206903448276, 91103202846976
Offset: 1
Examples
101 is a term since it can be split as 10^2 + 1^2 = 101. (This is so in any base.) 8833 is a term since it can be split as s=88 and t=33 with 88^2 + 33^2 = 8833.
References
- Frits Beukers, "Getallen - Een inleiding" (In Dutch), Epsilon Uitgaven, Amsterdam (2015).
Links
- A.H.M. Smeets, Table of n, a(n) for n = 1..5841
- Steven Charlton, List of terms, up to and including length 96 (unordered).
- Alf van der Poorten, Kurt Thomsen, and Mark Wiebe, A curious cubic identity and self similar sums of squares, The Mathematical Intelligencer, June 2007.
Formula
List of examples of regular languages that are subsets of this sequence (leading zeros must be omitted, and ^ denotes repetition of digit block(s)):
{(1232 8767)^(2*u) 1233 | n >= 0}; a(2) for u = 0, a(55) for u = 1, a(232) for u = 2, a(960) for u = 3, a(1320) for u = 4, a(3889) for u = 5.
{(8767 1232)^(2*u+1) 8768 | n >= 0}; a(14) for u = 0, a(93) for u = 1, a(395) for u = 2, a(1086) for u = 3
{(8832 1167)^(2*u) 8833 | n >= 0}; a(3) for u = 0, a(65) for u = 1, a(257) for u = 2, a(964) for u = 3, a(1328) for u = 4, a(4033) for u = 5.
{(1167 8832)^(2*u+1) 1168 | n >= 0}; a(12) for u = 0, a(85) for u = 1, a(386) for u = 2, a(1046) for u = 3
{(1167 8832)^(4*u+3) 1167 8833 | n >= 0}; a(230) for u = 0, a(1319) for u = 1
{(05882352 99117647)^(2*u) 05882353 | n >= 0}; a(6) for u = 0, a(276) for u = 1, a(3102) for u = 2.
{(94122352 05877647)^(2*u) 94122353 | n >= 0}; a(7) for u = 0, a(280) for u = 1, a(3122) for u = 2.
{(05877647 94122352)^(2*u+1) 05877648 | n >= 0}; a(76) for u = 0, a(1003) for u = 1, a(4067) for u = 2.
{(1765038124 8234961875)^(2*u) 1765038125 | n >= 0}; a(8) for u = 0, a(878) for u = 1, a(4493) for u = 2.
{(8234961875 1765038124)^(2*u+1) 8234961876 | n >= 0}; a(177) for u = 0, a(2672) for u = 1
{(2584043775 7415956224)^(2*u) 2584043776 | n >= 0}; a(9) for u = 0, a(886) for u = 1, a(4618) for u = 2.
{(7415956224 2584043775)^(2*u+1) 7415956225 | n >= 0}; a(170) for u = 0, a(2537) for u = 1.
{(7416043775 2583956224)^(2*u) 7416043776 | n >= 0}; a(10) for u = 0, a(924) for u = 1, a(5290) for u = 2.
{(2583956224 7416043775)^(2*u+1) 2583956225 | n >= 0}; a(126) for u = 0, a(1890) for u = 1.
{(8235038124 1764961875)^(2*u) 8235038125 | n >= 0}; a(11) for u = 0, a(932) for u = 1, a(5415) for u = 2.
{(1764961875 8235038124)^(2*u+1) 1764961876 | n >= 0}; a(119) for u = 0, a(1755) for u = 1.
{(123288328767 876711671232)^(2*u) 123288328768 | n >= 0}; a(13) for u = 0, a(1050) for u = 1.
{(876711671232 123288328767)^(2*u+1) 876711671233 | n >= 0}; a(254) for u = 0, a(4030) for u = 1.
{(1091314031180400 8908685968819599)^(2*u) 1091314031180401 | n >= 0}; a(30) for u = 0, a(3484) for u = 1.
{(2913840045440000 7086159954559999)^(2*u) 2913840045440001 | n >= 0}; a(34) for u = 0, a(3557) for u = 1.
Comments