A043037 -id:A043037 - cp's OEIS frontend

A067904 Primes of the form floor((3/2)^k).

2, 3, 5, 7, 11, 17, 4987, 7481, 180693856682317883, 4630985912862061063, 75677449184722757264165738713, 1910944005427272291238064043761449, 366425537175409658704814112327931286021

Offset: 1

Benoit Cloitre, Mar 03 2002

nonn

R. K. Guy, Unsolved Problems in Number Theory, E19.

Charles R Greathouse IV, Table of n, a(n) for n = 1..23

Cf. A043037, A070758, A070759.

f[n_]:=Floor[(3/2)^n]; lst={};Do[p=f[n];If[PrimeQ[p],AppendTo[lst,p]],{n,0,4*5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 02 2009 *)
Select[Floor[(3/2)^Range[300]],PrimeQ] (* Harvey P. Dale, Dec 28 2014 *)

v=[];for(k=2,5700, if(ispseudoprime(t=floor((3/2)^k)), v=concat(v,t))); v \\ Charles R Greathouse IV, Feb 15 2011

A261493 Palindromes that are concatenation of palindromic prime numbers in increasing order up to the n-th and then in decreasing order.

Original entry on oeis.org

2, 232, 23532, 2357532, 2357117532, 235711101117532, 235711101131101117532, 235711101131151131101117532, 235711101131151181151131101117532, 235711101131151181191181151131101117532, 235711101131151181191313191181151131101117532

Offset: 1

Altug Alkan, Aug 21 2015

Subsequence of A043037.

			For n=6, the first 6 palindromic primes are 2,3,5,7,11,101. Relevant subsequence that produce a(6) is 2,3,5,7,11,101,11,7,5,3,2. Concatenation of items with that order determines a(6) = 235711101117532.

Cf. A002385, A048677.

palQ[n_] := Reverse[idn = IntegerDigits@ n] == idn; s = Select[ Prime@ Range@ 1000, palQ]; f[n_] := FromDigits@ Flatten[ IntegerDigits@# & /@ Join[ Take[s, n], Reverse@ Take[s, n - 1]]]; Array[f, 11] (* Robert G. Wilson v, Aug 24 2015 *)

A337184 Numbers divisible by their first digit and their last digit.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 101, 102, 104, 105, 111, 112, 115, 121, 122, 123, 124, 125, 126, 128, 131, 132, 135, 141, 142, 144, 145, 147, 151, 152, 153, 155, 156, 161, 162, 164, 165, 168, 171, 172, 175, 181, 182

Offset: 1

Bernard Schott, Jan 29 2021

The first 23 terms are the same first 23 terms of A034838 then a(24) = 101 while A034838(24) = 111.
Terms of A034709 beginning with 1 and terms of A034837 ending with 1 are terms.
All positive repdigits (A010785) are terms.
There are infinitely many terms m for any of the 53 pairs (first digit, last digit) of m described below: when m begins with {1, 3, 7, 9} then m ends with any digit from 1 to 9; when m begins with {2, 4, 6, 8}, then m must also end with {2, 4, 6, 8}; to finish, when m begins with 5, m must only end with 5. - Metin Sariyar, Jan 29 2021

David A. Corneth, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Intersection of A034709 and A034837.
Subsequences: A010785\{0}, A034838, A043037, A043040, A208259, A066622.
Cf. A139138.

Select[Range[175], Mod[#, 10] > 0 && And @@ Divisible[#, IntegerDigits[#][[{1, -1}]]] &] (* Amiram Eldar, Jan 29 2021 *)

is(n) = n%10>0 && n%(n%10)==0 && n % (n\10^logint(n,10)) == 0 \\ David A. Corneth, Jan 29 2021

def ok(n): s = str(n); return s[-1] != '0' and n%int(s[0])+n%int(s[-1]) == 0
print([m for m in range(180) if ok(m)]) # Michael S. Branicky, Jan 29 2021

(10n-9)/9 <= a(n) < 45n. (I believe the liminf of a(n)/n is 3.18... and the limsup is 6.18....) - Charles R Greathouse IV, Nov 26 2024

Conjecture: 3n < a(n) < 7n for n > 75. - Charles R Greathouse IV, Dec 02 2024

A280828 Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.

Original entry on oeis.org

4, 22, 202

Offset: 1

Sergey Pavlov, Jan 08 2017

Let k=2*10^(n-1)+2, then a(n)=10^k+9. For all k>4, k is a term of A058441.
The only known terms from A088275 (Numbers n such that 10^n + 9 is prime) that are of the form 2*10^j + 2 are 4, 22, and 202; given the lower bound given for that sequence's next term, a(4) >= 200002. - Jon E. Schoenfield, Jan 11 2017
For n<4, let k=a(n) and p=(10^k-9)/10^(k/2)+3=10^(k/2)+3, then p is prime. - Sergey Pavlov, Jan 13 2017

			For n=1, a(1)=4 and 10^4 + 9 is prime.

Cf. A043037, A058441, A088275, A144249, A205529.

Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.

cp's OEIS Frontend

A067904 Primes of the form floor((3/2)^k).

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A261493 Palindromes that are concatenation of palindromic prime numbers in increasing order up to the n-th and then in decreasing order.

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A337184 Numbers divisible by their first digit and their last digit.

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A280828 Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.

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