A124362 -id:A124362 - cp's OEIS frontend

A124262 a(n) is the largest prime < 10*a(n-1) for n > 1, with a(1) = 2.

2, 19, 181, 1801, 17989, 179849, 1798487, 17984833, 179848309, 1798483067, 17984830667, 179848306667, 1798483066669, 17984830666651, 179848306666507, 1798483066665031, 17984830666650269, 179848306666502647, 1798483066665026389, 17984830666650263887, 179848306666502638867

Offset: 1

Artur Jasinski, Dec 16 2006

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000, extending and correcting a b-file from Artur Jasinski

Cf. A126031, A126041, A124475.
Sequences for other powers of 10: A124339 (100), A124361 (1000), A124364 (10000), A124362 (100000), A124368 (1000000).
Sequences for initial term k: A124263 (k=3), A124267 (5), A124291 (7), A124290 (11), A124298 (13), A124299 (17), A124336 (23), A124310 (29), A124335 (31), A124337 (37), A124338 (41).

NestList[NextPrime[10 #, -1]&, 2, 20] (* Vincenzo Librandi, Jun 28 2014 *)

step(k)=precprime(10*k)
my(t=1/5); vector(10,n,t=step(t)) \\ Charles R Greathouse IV, Sep 14 2015

A126031 a(n) is the largest prime < 3*a(n-1) for n > 1, with a(1) = 2.

Original entry on oeis.org

2, 5, 13, 37, 109, 317, 947, 2837, 8501, 25471, 76403, 229199, 687593, 2062759, 6188263, 18564769, 55694299, 167082893, 501248653, 1503745949, 4511237741, 13533713213, 40601139629, 121803418861, 365410256543, 1096230769619, 3288692308841, 9866076926507, 29598230779511

Offset: 1

Artur Jasinski, Dec 16 2006

nonn

Artur Jasinski, Table of n, a(n) for n = 1..40

Similar sequences for a(n) = largest prime < m*a(n-1): A006992 (m=2), this sequence (3), A124190 (4), A126033 (5), A126034 (6), A126035 (7), A126036 (8), A126037 (9), A124262 (10), A126039 (11), A126040 (12), A124339 (100), A124361 (1000), A124364 (10000), A124362 (100000), A124368 (1000000).

NestList[NextPrime[3#,-1]&,2,30] (* Harvey P. Dale, Feb 03 2012 *)

A124365 Numbers that raised to only one specific exponent gives a result for which the sum of its digits is equal to number itself.

Original entry on oeis.org

2, 3, 4, 5, 6, 17, 20, 22, 25, 26, 31, 34, 35, 40, 43, 45, 53, 58, 63, 64, 68, 71, 81, 82, 85, 86, 91, 94, 97, 98, 103, 104, 117

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, Oct 30 2006

Subset of A124359

			31^7=27512614111 and 2+7+5+1+2+6+1+4+1+1+1=31. This is possible only with 7 as exponent.
97^10=73742412689492826049 and 7+3+7+4+2+4+1+2+6+8+9+4+9+2+8+2+6+4+9=97. This is possible only with 10 as exponent.

Cf. A124359, A124360, A124361, A124362, A046019, A124364.

A124366 Consecutive numbers n and (n+1) that raised to the same exponent m produce two numbers for which the sum of their digits gives n and (n+1).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 17, 18, 35, 36, 103, 104, 106, 107, 108, 134, 135, 256, 257, 295, 296, 298, 299, 306, 307, 386, 387, 421, 422, 468, 469, 575, 576, 792, 793, 865, 866, 962, 963, 1008, 1009, 1061, 1062, 1476, 1477, 1495, 1496, 2032, 2033, 2376, 2377

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, Oct 30 2006

			17^3=4913 (4+9+1+3=17) and 18^3=5832 (5+8+3+2=18)
306^26= 42536043213832457558766474492498614961439017908885402928656941056
(sum of the digits equal to 306) and
307^26= 46301788027092145989912680349353041288862842956233592928809850249
(sum of the digits equal to 307)

Cf. A124359, A124360, A124361, A124362, A046019, A124364, A124365.

cp's OEIS Frontend

A124262 a(n) is the largest prime < 10*a(n-1) for n > 1, with a(1) = 2.

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A126031 a(n) is the largest prime < 3*a(n-1) for n > 1, with a(1) = 2.

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A124365 Numbers that raised to only one specific exponent gives a result for which the sum of its digits is equal to number itself.

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A124366 Consecutive numbers n and (n+1) that raised to the same exponent m produce two numbers for which the sum of their digits gives n and (n+1).

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