Original entry on oeis.org
23, 4567891, 23456789, 1234567891, 23456789123456789, 23456789123456789123, 4567891234567891234567891, 1234567891234567891234567891, 7891234567891234567891234567891
Offset: 1
A075766
Numbers k such that A007923(k) is prime.
Original entry on oeis.org
2, 7, 8, 10, 17, 20, 25, 28, 31, 38, 61, 62, 355, 4690, 4772, 8162, 10523, 14716, 32114, 117712
Offset: 1
- Jason Earls, Some Results Concerning the Smarandache Deconstructive Sequence, Smarandache Notions Journal, Volume 14 Issue 1, January 2004, Pages 222-226.
- Shyam Sunder Gupta, Primes in the Smarandache deconstructive sequence, Scientia Magna Vol. 2 (2006), No. 3, 26-30. Reports the three probable primes for k= 4690, 4772, and 8162.
- Shyam Sunder Gupta, Memorable Prime, Number Theory Mailing List, Mar 07 2024. Reports the 32114-digit prime.
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isok(n) = my(m=(n*(n+1)/2-1)%9+1); isprime(sum(k=0, n-1, 10^k*((m-k-1)%9+1))); \\ Michel Marcus, May 30 2017
A066547
Let N = 123456789101112131415161718..., the concatenation of the natural numbers. a(n) is the n-digit number formed from the digits of N starting from the {n(n-1)/2 +1}th digit. Omit any leading zeros.
Original entry on oeis.org
1, 23, 456, 7891, 1112, 131415, 1617181, 92021222, 324252627, 2829303132, 33343536373, 839404142434, 4454647484950, 51525354555657, 585960616263646, 5666768697071727, 37475767778798081, 828384858687888990, 9192939495969798991, 101102103104105106, 107108109110111112113
Offset: 1
1, 23, 456, 7891, 01112, 131415, 1617181, 92021222, 3... becomes 1, 23, 456, 7891, 1112, 131415, 1617181, 92021222, ...
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d = Flatten[IntegerDigits /@ Range[90]]; Table[FromDigits[Take[d, {n(n + 1)/2 + 1, (n + 1)(n + 2)/2}]], {n, 0, 17}] (* Robert G. Wilson v, Nov 22 2004 *)
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N=[]; k=0; for(n=1,20, while(#NM. F. Hasler, May 08 2014
More terms from Larry Reeves (larryr(AT)acm.org), Dec 18 2001
A001369
Blocks of increasing length using 1,2,3,...,9,10; omit leading 0's.
Original entry on oeis.org
1, 23, 456, 7891, 1234, 567891, 123456, 78910123, 456789101, 2345678910, 12345678910, 123456789101, 2345678910123, 45678910123456, 789101234567891, 123456789101234, 56789101234567891, 12345678910123456, 7891012345678910123, 45678910123456789101
Offset: 1
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nn = 20; d = Flatten[Table[{1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0}, {Ceiling[nn (nn + 1)/22]}]]; Table[e = (n + 1) n/2; s = e - n + 1; FromDigits[d[[s ;; e]]], {n, nn}] (* T. D. Noe, Apr 05 2011 *)
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N=[]; k=Mod(-1,10); for(n=1, 20, while(#NM. F. Hasler, May 08 2014
A081549
a(1) = 1; for n > 1, a(n) > a(n-1) is the smallest number such that the concatenation a(1)a(2)a(3)... forms a cyclic concatenation of 123456789 (of nonzero digits).
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 34, 56, 78, 91, 234, 567, 891, 2345, 6789, 12345, 67891, 234567, 891234, 5678912, 34567891, 234567891, 2345678912, 3456789123, 4567891234, 5678912345, 6789123456, 7891234567, 8912345678, 9123456789
Offset: 1
Cf.
A165307 (non-monotonic version),
A007923 (version with strictly increasing length).
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a = {1}; c = 0; Do[c = 10 c + Mod[n, 9] + 1; If[c > a[[-1]], AppendTo[a, c]; c = 0], {n, 170}]; a (* Ivan Neretin, Aug 14 2015 *)
A100814
Digits 9 to 0 are written in order with increasing number of digits for each member of the sequence. Leading zeros are counted, but are not written down.
Original entry on oeis.org
9, 87, 654, 3210, 98765, 432109, 8765432, 10987654, 321098765, 4321098765, 43210987654, 321098765432, 1098765432109, 87654321098765, 432109876543210, 9876543210987654, 32109876543210987, 654321098765432109
Offset: 1
The first number in the sequence is 9.
The second number in the sequence is 87.
The third number in the sequence is 654.
- C. Ashbacher, "Some problems concerning the Smarandache deconstructive sequence", Journal of Recreational Mathematics, vol. 29(2), 82-84 (1998)
- Russell Euler and Jawad Sadek, "Some divisibility patterns in the Smarandache deconstructive sequence", Journal of Recreational Mathematics, vol. 31(1), 12-14 (2002-2003)
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With[{c=PadRight[{},250,Range[9,0,-1]]},Table[FromDigits[Take[c,{(n(n+1))/2+1,((n+1)(n+2))/2}]],{n,0,20}]] (* Harvey P. Dale, Jan 17 2017 *)
Showing 1-6 of 6 results.
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