A317903
a(n) = A038394(n)^^A038394(n) (mod 10^len(A038394(n))), where ^^ indicates tetration or hyper-4 (e.g., 3^^4=3^(3^(3^3))).
Original entry on oeis.org
4, 76, 176, 4176, 314176, 91314176, 891314176, 80891314176, 88080891314176, 5288080891314176, 705288080891314176, 10705288080891314176, 2410705288080891314176, 912410705288080891314176, 42912410705288080891314176, 9242912410705288080891314176, 989242912410705288080891314176
Offset: 1
For n = 6, a(6) = 13117532^^13117532 (mod 10^8) == 91314176.
- Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, page 60. ISBN 978-88-6178-789-6
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tmod(b, n) = {if (b % n == 0, return (0)); if (b % n == 1, return (1)); if (gcd(b, n)==1, return (lift(Mod(b, n)^tmod(b, lift(znorder(Mod(b, n))))))); lift(Mod(b, n)^(eulerphi(n) + tmod(b, eulerphi(n))));}
f(n) = fromdigits(concat([digits(p) | p<-Vecrev(primes(n))])); \\ A038394
a(n) = if (n==1, 4, my(x=f(n)); tmod(x, 10^#Str(x))); \\ Michel Marcus, Sep 12 2021
A019518
Smarandache-Wellin numbers: a(n) is the concatenation of first n primes (written in base 10).
Original entry on oeis.org
2, 23, 235, 2357, 235711, 23571113, 2357111317, 235711131719, 23571113171923, 2357111317192329, 235711131719232931, 23571113171923293137, 2357111317192329313741, 235711131719232931374143, 23571113171923293137414347
Offset: 1
E.g. a(6) = 2_3_5_7_11_13 = 23571113.
- R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 72. [The 2002 printing states incorrectly that a(719) is prime. Cf. A046035.] This book uses the name "Smarandache-Wellin numbers", referring to a 1998 private communication from P. Wellin.
- H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.
- M. Le, On Smarandache Concatenated Sequences I: Prime Power Sequences, Smarandache Notions Journal, Vol. 9, No. 1-2, 1998, 129-130.
- S. Smarandoiu, Convergence of Smarandache continued fractions, Abstract 96T-11-195, Abstracts Amer. Math. Soc., 17 (No. 4, 1996), 680.
- Reinhard Zumkeller, Table of n, a(n) for n = 1..300
- M. Fleuren, Factoring of the Smarandache Concatenated Prime Sequence.
- F. Smarandache, Collected Papers, Vol. II, Tempus Publ. Hse., Bucharest, Romania, 1996.
- Eric Weisstein's World of Mathematics, Consecutive Number Sequences
- Eric Weisstein's World of Mathematics, Copeland-Erdős Constant
- Index entries for sequences related to Most Wanted Primes video
For the primes in this sequence see
A069151. For where the primes occur see
A046035.
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a019518 n = a019518_list !! (n-1)
a019518_list = map read $ scanl1 (++) $ map show a000040_list :: [Integer]
-- Reinhard Zumkeller, Mar 03 2014
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[Seqint(Reverse(&cat[Reverse(Intseq(NthPrime(k))): k in [1..n]])): n in [1..20]]; // Vincenzo Librandi, Aug 23 2015
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ConsecutivePrimes[n_] := FromDigits[Flatten[IntegerDigits /@ Prime[Range[n]]]] (* Eric W. Weisstein *)
Table[FromDigits[Flatten[IntegerDigits[Prime[Range[i]]]]],{i,15}] (* Jayanta Basu, May 30 2013 *)
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s="";for(n=1,30,print1(s=Str(s,prime(n))",")) \\ Cino Hilliard; simplified by M. F. Hasler, Oct 06 2013
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A019518(n)=eval(concat(concat([""],primes(n)))) \\ Faster than concat(apply(s->Str(s),primes(n))) or forprime(...s=Str(s,p)). - M. F. Hasler, Oct 06 2013
A038395
Concatenation of the first n odd numbers in reverse order.
Original entry on oeis.org
1, 31, 531, 7531, 97531, 1197531, 131197531, 15131197531, 1715131197531, 191715131197531, 21191715131197531, 2321191715131197531, 252321191715131197531, 27252321191715131197531, 2927252321191715131197531, 312927252321191715131197531
Offset: 1
M. I. Petrescu (mipetrescu(AT)yahoo.com)
- Mihaly Bencze [Beneze] and L. Tutescu, Some Notions and Questions in Number Theory, Sequence 3.
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Table[FromDigits[Flatten[IntegerDigits/@Join[Reverse[Range[1,n,2]]]]], {n,1,29,2}] (* Harvey P. Dale, Jun 02 2011 *)
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t=""; for( n=1,10^3, ( t=eval( Str( 2*n-1,t))) & print(n" "t)) \\ M. F. Hasler, Apr 13 2008
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def a(n): return int("".join(map(str, range(2*n-1, 0, -2))))
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Jan 31 2021
A092844
a(n) = Sum_{k=1..n} prime(k)*10^(k-1).
Original entry on oeis.org
2, 32, 532, 7532, 117532, 1417532, 18417532, 208417532, 2508417532, 31508417532, 341508417532, 4041508417532, 45041508417532, 475041508417532, 5175041508417532, 58175041508417532, 648175041508417532
Offset: 1
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ListTools:-PartialSums([seq(ithprime(i)*10^(i-1),i=1..30)]); # Robert Israel, Apr 12 2020
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Array[Sum[Prime[k]*10^(k - 1), {k, #}] &, 17] (* Michael De Vlieger, Jun 22 2022 *)
Accumulate[Table[Prime[n]10^(n-1),{n,20}]] (* Harvey P. Dale, Oct 11 2022 *)
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a(n) = fromdigits(Vecrev(primes(n))); \\ Kevin Ryde, Jun 22 2022
Showing 1-4 of 4 results.
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