A120099 - OEIS

%I #13 Sep 25 2021 10:39:46

%S 17,45,87,101,112,230,270,341,468,472,473,479,517,554,555,568,650,657,

%T 663,696,718,727,810,830,836,900,917,952,984,988,1020,1021,1022,1059,

%U 1140,1142,1167,1200,1295,1326,1400,1401,1405,1406,1418,1449,1499,1503,1526

%N Numbers n such that the closest primes surrounding 10^n are the same distance modulo 100.

%C 17 {3, 3}, 45 {9, 9}, 87 {373, 273}, 101 {3, 203}, 112 {207, 807}, 230 {753, 1053}, 270 {361, 861}, 341 {831, 1331}, 468 {301, 801}, 472 {1569, 2669}, 473 {99, 599}, 479 {109, 209}, 554 {937, 437}, 555 {151, 2151}, 568 {501, 801}, 650 {1999, 899}, 657 {1791, 291}, 663 {6333, 33},

%C 696 {61, 1361}, 718 {5863, 1463}, 727 {273, 1073}, 810 {1591, 2891}, 830 {2853, 1253}, 836 {2809, 1209}, 900 {1873, 773}, 917 {693, 5393}, 952 {4827, 27}, 984 {1867, 2867}, 988 {753, 1053}, 1020 {793, 1193}, 1021 {1609, 6209}, 1022 {853, 1053} 1059 {5793, 1293}, 1140 {357, 4857},

%C 1142 {4329, 5829}, 1167 {1131, 3231}, 1200 {5227, 4127}, 1295 {5169, 2369}, 1326 {907, 4007}, 1400 {13317, 2517}, 1401 {10549, 2249}, 1405 {4329, 629}, 1406 {7477, 10277}, 1418 {841, 8741}, 1449 {2989, 3089}, 1499 {2001, 1901}, 1503 {439, 339}, 1526 {4603, 603}, 1534 {2409, 3209}, ...,.

%F A033873 (mod 100) == A033874 (mod 100).

%t NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ@k, k++ ]; k]; PrevPrim[n_] := Block[{k = n - 1}, While[ ! PrimeQ@k, k-- ]; k]; Do[ If[ Mod[ NextPrim[10^n], 100] == Mod[10^n - PrevPrim[10^n], 100], Print[{n, a, b}]], {n, 1320}]

%t Select[Range[1530],Mod[NextPrime[10^#]-10^#,100]==Mod[10^# -NextPrime[ 10^#,-1],100]&] (* _Harvey P. Dale_, Sep 24 2021 *)

%Y Cf. A115564, A118798.

%K base,less,nonn

%O 1,1

%A _Cino Hilliard_ and _Robert G. Wilson v_, Jun 08 2006

%E More terms from _Robert G. Wilson v_, Jun 09 2006

%E Corrected (term 517 added) by _Harvey P. Dale_, Sep 25 2021