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A118798 Numbers n such that the closest primes surrounding 10^n have the same last two digits. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 13 17:09 EDT 2021. Contains 345008 sequences. (Running on oeis4.)