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A120099
Numbers n such that the closest primes surrounding 10^n are the same distance modulo 100.
0
17, 45, 87, 101, 112, 230, 270, 341, 468, 472, 473, 479, 517, 554, 555, 568, 650, 657, 663, 696, 718, 727, 810, 830, 836, 900, 917, 952, 984, 988, 1020, 1021, 1022, 1059, 1140, 1142, 1167, 1200, 1295, 1326, 1400, 1401, 1405, 1406, 1418, 1449, 1499, 1503, 1526
OFFSET
1,1
COMMENTS
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},
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},
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}, ...,.
FORMULA
A033873 (mod 100) == A033874 (mod 100).
MATHEMATICA
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}]
Select[Range[1530], Mod[NextPrime[10^#]-10^#, 100]==Mod[10^# -NextPrime[ 10^#, -1], 100]&] (* Harvey P. Dale, Sep 24 2021 *)
CROSSREFS
Sequence in context: A140155 A221752 A032698 * A307293 A045570 A058205
KEYWORD
base,less,nonn
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Jun 09 2006
Corrected (term 517 added) by Harvey P. Dale, Sep 25 2021
STATUS
approved