A118798 Numbers n such that the closest primes surrounding 10^n have the same last two digits.

79, 178, 179, 186, 210, 284, 300, 349, 391, 456, 594, 595, 599, 624, 645, 654, 659, 704, 712, 713, 860, 871, 892, 904, 924, 990, 1015, 1089, 1097, 1110, 1118, 1151, 1165, 1374, 1396, 1459, 1709, 1721, 1826, 1831, 1911, 1943, 1956, 2005, 2061, 2082, 2089

Offset

1,1

Comments

79 {251, 49}, 178 {239, 261}, 179 {221, 979}, 186 {479, 721}, 210 {171, 1129}, 284 {467, 133}, 300 {69, 331}, 349 {2603, 297}, 391 {123, 477}, 456 {633, 567}, 594 {11, 789}, 595 {503, 297}, 599 {2339, 2161}, 624 {413, 187}, 645 {3291, 109}, 654 {1811, 1089}, 659 {2363, 937}, 704 {3489, 211},

712 {171, 1029}, 713 {801, 2299}, 860 {1193, 2907}, 871 {827, 1473}, 892 {629, 271}, 904 {503, 597}, 924 {303, 4797}, 990 {3, 1197}, 1015 {71, 1029}, 1089 {4403, 5997}, 1097 {2271, 1429}, 1110 {2373, 2527}, 1118 {1767, 2233}, 1151 {2703, 97}, 1165 {33, 3867}, 1374 {689, 1411},

1396 {1023, 3477}, 1459 {10211, 489}, 1709 {2859, 4241}, 1721 {10311, 189}, 1826 {1761, 1539}, 1831 {17751, 1449}, 1911 {4179, 2621}, 1943 {1279, 1721}, 1956 {541, 9459}, 2005 {141, 14259}, 2061 {6607, 3293}, 2082 {9537, 4563}, 2089 {597, 203}, 2091 {2517, 9783}, 2135 {7287, 3513}, ...,.

Links

Table of n, a(n) for n=1..47.

V. Danilov, Smallest and largest n-digit primes.n

Formula

A033873 + A033874 == 0 (mod 100). - Robert G. Wilson v, May 27 2006

Example

79 is in the sequence since the two primes nearest primes 10^79 are 10^79 - 251 and 10^79 + 49.

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ@k, k++ ]; k]; PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ@k, k-- ]; k]; fQ[n_] := Mod[NextPrim[10^n], 100] == Mod[PrevPrim[10^n], 100]; Do[ If[ fQ@n, Print@n], {n, 2, 1250}] (* Robert G. Wilson v, May 27 2006 *)
Select[Range[2100], Mod[NextPrime[10^#], 100]==Mod[NextPrime[10^#, -1], 100]&] (* Harvey P. Dale, Mar 09 2019 *)

Prog

(PARI) g(n) = for(j=1, n, x=precprime(10^j); y=nextprime(10^j); if(x%100==y%100, print1 (j", ")))

Crossrefs

Cf. A115564.

Sequence in context: A142307 A142383 A033673 * A082929 A044411 A044792

Adjacent sequences: A118795 A118796 A118797 * A118799 A118800 A118801

Keyword

easy,nonn,base,less

Author

Cino Hilliard, May 23 2006

Extensions

More terms from Robert G. Wilson v, May 27 2006 - Jun 14 2006

Status

approved