A155658
a(n) = 11^n + 7^n - 1.
Original entry on oeis.org
1, 17, 169, 1673, 17041, 177857, 1889209, 20310713, 220123681, 2398301297, 26219899849, 287288997353, 3152269663921, 34619601154337, 380428056656089, 4181995730925593, 45982962794141761, 505679659013280977
Offset: 0
Cf.
A155638,
A155639,
A155640,
A155641,
A155642,
A155643,
A155644,
A155645,
A155646,
A155647,
A155648,
A155649,
A155650,
A155651,
A155652,
A155653,
A155654,
A155655,
A155656,
A155657.
A155644
a(n) = 11^n-5^n+1.
Original entry on oeis.org
1, 7, 97, 1207, 14017, 157927, 1755937, 19409047, 213968257, 2355994567, 25927658977, 285262842487, 3138184236097, 34521491440807, 379743730067617, 4177217651837527, 45949577275681537, 505446265559840647
Offset: 0
Cf.
A155628,
A155629,
A155630,
A155631,
A155632,
A155633,
A155634,
A155635,
A155636,
A155637,
A155638,
A155639,
A155640,
A155641,
A155642,
A155643.
-
Table[11^n-5^n+1,{n,0,20}] (* or *) LinearRecurrence[{17, -71, 55}, {1, 7, 97}, 20] (* Harvey P. Dale, Jul 11 2011 *)
-
a(n)=11^n-5^n+1 \\ Charles R Greathouse IV, Jun 11 2015
Original entry on oeis.org
1, 5, 65, 785, 8705, 92225, 953345, 9720065, 98320385, 989922305, 9939533825, 99637202945, 997823217665, 9986939305985, 99921635835905, 999529815015425, 9997178890092545, 99983073340555265, 999898440043331585
Offset: 0
Cf.
A155630,
A155631,
A155632,
A155633,
A155634,
A155635,
A155636,
A155637,
A155638,
A155639,
A155640,
A155641,
A155642,
A155643,
A155644,
A155645,
A155646,
A155647,
A155648,
A155649,
A155650,
A155651,
A155652.
A155659
a(n) = 8^n - 7^n + 1.
Original entry on oeis.org
1, 2, 16, 170, 1696, 15962, 144496, 1273610, 11012416, 93864122, 791266576, 6612607850, 54878189536, 452866803482, 3719823438256, 30436810578890, 248242046141056, 2019169299698042, 16385984911571536, 132716292890482730, 1073129238309234976, 8664826172771491802
Offset: 0
Cf.
A155638,
A155639,
A155640,
A155641,
A155642,
A155643,
A155644,
A155645,
A155646,
A155647,
A155648,
A155649,
A155650,
A155651,
A155652,
A155653,
A155654,
A155655,
A155656,
A155657,
A155658.
A155645
a(n) = 7^n+6^n-1.
Original entry on oeis.org
1, 12, 84, 558, 3696, 24582, 164304, 1103478, 7444416, 50431302, 342941424, 2340123798, 16018069536, 109949704422, 756587236944, 5217746494518, 36054040477056, 249557173431942, 1729973554578864, 12008254925383638
Offset: 0
Cf.
A155628,
A155629,
A155630,
A155631,
A155632,
A155633,
A155634,
A155635,
A155636,
A155637,
A155638,
A155639,
A155640,
A155641,
A155642,
A155643,
A155644.
-
Table[7^n+6^n-1,{n,0,20}] (* or *) LinearRecurrence[{14,-55,42},{1,12,84},20] (* Harvey P. Dale, May 08 2012 *)
-
a(n)=7^n+6^n-1 \\ Charles R Greathouse IV, Jun 11 2015
A155660
a(n) = 9^n - 7^n + 1.
Original entry on oeis.org
1, 3, 33, 387, 4161, 42243, 413793, 3959427, 37281921, 347066883, 3204309153, 29403732867, 268588249281, 2444976817923, 22198569382113, 201143570584707, 1819787258282241, 16444551185679363, 148466221699088673, 1339452822487618947, 12077873192759316801, 108860443267429075203
Offset: 0
Cf.
A155638,
A155639,
A155640,
A155641,
A155642,
A155643,
A155644,
A155645,
A155646,
A155647,
A155648,
A155649,
A155650,
A155651,
A155652,
A155653,
A155654,
A155655,
A155656,
A155657,
A155658,
A155659.
A155661
a(n) = 10^n - 7^n + 1.
Original entry on oeis.org
1, 4, 52, 658, 7600, 83194, 882352, 9176458, 94235200, 959646394, 9717524752, 98022673258, 986158712800, 9903110989594, 99321776927152, 995252438490058, 9966767069430400, 99767369486012794, 998371586402089552
Offset: 0
Cf.
A155638,
A155639,
A155640,
A155641,
A155642,
A155643,
A155644,
A155645,
A155646,
A155647,
A155648,
A155649,
A155650,
A155651,
A155652,
A155653,
A155654,
A155655,
A155656,
A155657,
A155658,
A155659,
A155660.
-
Table[10^n-7^n+1,{n,0,20}] (* or *) LinearRecurrence[{18,-87,70},{1,4,52}, 21] (* Harvey P. Dale, May 05 2011 *)
-
a(n)=10^n-7^n+1 \\ Charles R Greathouse IV, Jun 11 2015
A155662
a(n) = 11^n - 7^n + 1.
Original entry on oeis.org
1, 5, 73, 989, 12241, 144245, 1653913, 18663629, 208594081, 2317594085, 25654949353, 283334343869, 3124587089521, 34425823133525, 379071610510393, 4172500607905709, 45916496933002561, 505214397985306565, 5558288899894321033, 61147691553229173149
Offset: 0
Cf.
A155638,
A155639,
A155640,
A155641,
A155642,
A155643,
A155644,
A155645,
A155646,
A155647,
A155648,
A155649,
A155650,
A155651,
A155652,
A155653,
A155654,
A155655,
A155656,
A155657,
A155658,
A155659,
A155660,
A155661.
A217696
Let p = A002145(n) be the n-th prime of the form 4k+3, then a(n) is the smallest number such that p is the smallest prime of the form 4k+3 for which 4*a(n)+2-p is prime.
Original entry on oeis.org
1, 4, 10, 24, 76, 102, 196, 74, 104, 348, 314, 345, 86, 660, 443, 1494, 914, 1329, 2613, 1635, 1316, 1856, 1688, 2589, 2628, 6423, 3116, 2165, 6320, 4445, 7278, 4743, 16539, 17783, 6084, 3806, 6281, 8946, 15129, 6266, 10976, 19538, 16794, 31160, 32916, 57041
Offset: 1
n=1: the first prime in the form of 4k+3 is 3, 3+3=6=4*1+2, so a(1)=1;
n=2: the second prime in the form of 4k+3 is 7, 7+7=14=3+11=4*3+2, and 11 is also a prime in the form of 4k+3, so a(2)!=3. 7+11=18=4*4+2=3+15, and 15 is not a prime number. So a(2)=4.
-
goal = 46; plst = {}; pct = 0; clst = {}; n = -1; While[pct < goal,
n = n + 4; If[PrimeQ[n], AppendTo[plst, n]; AppendTo[clst, 0];
pct++]]; n = 2; cct = 0; While[cct < goal, n = n + 4; p1 = n + 1;
While[p1 = p1 - 4; p2 = n - p1; ! ((PrimeQ[p1]) && (PrimeQ[p2]) && (Mod[p2, 4] == 3))]; If[MemberQ[plst, p2], If[id = Position[plst, p2][[1, 1]]; clst[[id]] == 0, clst[[id]] = (n - 2)/4; cct++]]]; clst
-
ok(n,p)=if(!isprime(n-p),return(0));forprime(q=2,p-1,if(q%4==3 && isprime(n-q),return(0)));1
a(n)=my(p,k); forprime(q=2,,if(q%4==3&&n--==0,p=q;break)); k=(p+1)/4; while(!ok(4*k+2,p),k++); k \\ Charles R Greathouse IV, Mar 19 2013
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