A218713
a(n) is smallest number such that a(n)^2 + 1 is divisible by 37^n.
Original entry on oeis.org
0, 6, 117, 9466, 800982, 6423465, 756360062, 24900904028, 1019349744435, 15069267560119, 794839706330581, 71333925879937154, 2419512779032508628, 116073623326088126430, 359642847542169431827, 144552623583462302226851, 3523356323886506075746572
Offset: 0
a(3) = 9466 because 9466^2+1 = 29 * 37 ^ 3 * 61.
-
b=6;n37=37;jo=Join[{0,b},Table[n37=37*n37;b=PowerMod[b,37,n37];b=Min[b,n37-b],{99}]]
A218714
a(n) is smallest number such that a(n)^2 + 1 is divisible by 41^n.
Original entry on oeis.org
0, 9, 378, 11389, 1251967, 46464143, 2363588163, 92615568742, 287369842623, 112076323050317, 2403749863808044, 56094387104417648, 1156752450536914530, 43970228150195457632, 10132163897314954464899, 503212117431217218892992, 19164391897329672149556204
Offset: 0
a(3) = 11389 because 11389^2+1 = 2 * 41 ^ 3 * 941.
-
b=9;n41=41;jo=Join[{0,b},Table[n41=41*n41;b=PowerMod[b,41,n41];b=Min[b,n41-b],{99}]]
A218715
a(n) is smallest number such that a(n)^2 + 1 is divisible by 53^n.
Original entry on oeis.org
0, 23, 500, 27590, 623098, 23048345, 5041394261, 416081467190, 11331029931180, 50928660480181, 6548598523124085, 2441875986594058601, 76594163421571591377, 7783548304686046882879, 252583670951378815076851, 4392422457122810120236558, 1165802007767335105471573954
Offset: 0
a(3) = 27590 because 27590^2+1 = 53 ^ 3 * 5113.
-
b=23;n53=53;jo=Join[{0,b},Table[n53=53*n53;b=PowerMod[b,53,n53];b=Min[b,n53-b],{99}]]
A218716
a(n) is smallest number such that a(n)^2 + 1 is divisible by 61^n.
Original entry on oeis.org
0, 11, 682, 51412, 6304056, 144762466, 9435321777, 988322434636, 71294762793847, 3138611770750343, 283798117998769727, 15409745938584647495, 320007169218635518122, 45443939732277600209579, 207359227164430355867160, 59053635973003478214807486
Offset: 0
a(3) = 51412 because 51412^2+1 = 5 * 17 * 61 ^ 3 * 137.
-
b=11;n61=61;jo=Join[{0,b},Table[n61=61*n61;b=PowerMod[b,61,n61];b=Min[b,n61-b],{99}]]
A218717
a(n) is smallest number such that a(n)^2 + 1 is divisible by 73^n.
Original entry on oeis.org
0, 27, 776, 153765, 6459524, 404034898, 41865466758, 3219884218827, 239822883201307, 9110883894036198, 991706090146518323, 142813358470363920740, 8641533837443707913816, 586811715371303018585730, 2756887299416274753296336, 729513196939063257288876118
Offset: 0
a(3) = 153765 because 153765^2+1 = 2 * 73 ^ 3 * 30389.
-
b=27;n73=73;jo=Join[{0,b},Table[n73=73*n73;b=PowerMod[b,73,n73];b=Min[b,n73-b],{99}]]
A218718
a(n) is smallest number such that a(n)^2 + 1 is divisible by 89^n.
Original entry on oeis.org
0, 34, 3861, 344464, 20099637, 2153335831, 102666405913, 4867146503697, 923990886302412, 50251663587824641, 5655954122907587985, 909925832091926912414, 85120439454684773642745, 2631773999763198769695986, 41332517834853462204330752
Offset: 0
a(3) = 344464 because 344464^2+1 = 37 * 89 ^ 3 * 4549.
Cf.
A002522,
A049532,
A034939,
A218709,
A218710,
A218712,
A218713,
A218714,
A218715,
A218716,
A218717.
-
b=34;n89=89;jo=Join[{0,b},Table[n89=89*n89;b=PowerMod[b, 89,n89];b=Min[b,n89-b],{99}]]
A218719
a(n) is smallest number such that a(n)^2 + 1 is divisible by 97^n.
Original entry on oeis.org
0, 22, 4052, 107551, 22709274, 331407850, 197177418061, 26457926739667, 2369608176604944, 76004727767164666, 25163629663367816827, 1965881512952938486496, 191165497320828772935835, 21700278688179406782082106, 560121950820639295011033922
Offset: 0
a(3) = 107551 because 107551^2+1 = 2 * 97 ^ 3 * 6337.
Cf.
A002522,
A049532,
A034939,
A218709,
A218710,
A218712,
A218713,
A218714,
A218715,
A218716,
A218717,
A218718.
-
b=22;n97=97;jo=Join[{0,b},Table[n97=97*n97;b=PowerMod[b, 97,n97];b=Min[b,n97-b],{99}]]
A218720
a(n) is smallest number such that a(n)^2 + 1 is divisible by 101^n.
Original entry on oeis.org
0, 10, 515, 296344, 35764191, 1108900220, 316411915250, 47023298541694, 3156215819652023, 310872228812491206, 28124944860980892220, 3783840171259076226254, 208193145695151069244665, 19364218657938636320485082, 663491749602035014400202724
Offset: 0
a(3) = 296344 because 296344^2+1 = 101 ^ 3 * 85237.
Cf.
A002522,
A049532,
A034939,
A218709,
A218710,
A218712,
A218713,
A218714,
A218715,
A218716,
A218717,
A218718,
A218719.
-
b=10;n101=101;jo=Join[{0,b},Table[n101=101*n101;b=PowerMod[b, 101,n101];b=Min[b,n101-b],{99}]]
Showing 1-8 of 8 results.