A120099 Numbers n such that the closest primes surrounding 10^n are the same distance modulo 100.

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}, ...,.

Links

Table of n, a(n) for n=1..49.

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

Cf. A115564, A118798.

Sequence in context: A140155 A221752 A032698 * A307293 A045570 A058205

Adjacent sequences: A120096 A120097 A120098 * A120100 A120101 A120102

Keyword

base,less,nonn

Author

Cino Hilliard and Robert G. Wilson v, Jun 08 2006

Extensions

More terms from Robert G. Wilson v, Jun 09 2006

Corrected (term 517 added) by Harvey P. Dale, Sep 25 2021

Status

approved