A066622 -id:A066622 - cp's OEIS frontend

A138143 Triangle read by rows in which row n lists p(1), p(2), ..., p(n), p(n-1), ..., p(1), where p(i) = i-th prime.

2, 2, 3, 2, 2, 3, 5, 3, 2, 2, 3, 5, 7, 5, 3, 2, 2, 3, 5, 7, 11, 7, 5, 3, 2, 2, 3, 5, 7, 11, 13, 11, 7, 5, 3, 2, 2, 3, 5, 7, 11, 13, 17, 13, 11, 7, 5, 3, 2, 2, 3, 5, 7, 11, 13, 17, 19, 17, 13, 11, 7, 5, 3, 2, 2, 3, 5, 7, 11, 13, 17, 19, 23, 19, 17, 13, 11, 7, 5, 3, 2, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2

Offset: 1

Omar E. Pol, Mar 09 2008

Row n contains 2n-1 terms and each column lists the prime numbers A000040.

Triangle of primes mentioned in A061802.

			Triangle begins:
.............. 2
........... 2, 3, 2
........ 2, 3, 5, 3, 2
..... 2, 3, 5, 7, 5, 3, 2
.. 2, 3, 5, 7,11, 7, 5, 3, 2

Cf. A000040, A061802, A066622, A037126.

nn=10;Module[{pr=Prime[Range[nn]],e},Flatten[Table[e=Take[pr,n];Join[ e,Reverse[Most[e]]],{n,nn}]]] (* Harvey P. Dale, Mar 14 2015 *)

Edited by N. J. A. Sloane, Apr 07 2008, Nov 15 2008

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

A173586 Decimal values a(n) of the binary numbers b(n) obtained by starting from first prime number (2), sequentially concatenating the binary representation of all prime numbers till n-th prime, and after that, sequentially concatenating the binary representation of all prime numbers, from (n-1)th till the first prime.

Original entry on oeis.org

2, 46, 1502, 96222, 12316638, 3153031134, 1614350348254, 1653094690025438, 1692768964130074590, 1733395419356639752158, 1774996909423485572837342, 3635193670499109531489365982

Offset: 1

Umut Uludag, Feb 22 2010

			a(1)=binary_to_decimal(10)=2, a(2)=binary_to_decimal(101110)=46, a(3)=binary_to_decimal(10111011110)=1502, a(4)=binary_to_decimal(10111011111011110)=96222 etc.

Cf. A066622. This sequence uses the term generation rule of A066622 (Concatenation of prime numbers in increasing order up to the n-th and then in decreasing order.), albeit with the binary base instead of the decimal base.

a(n) = binary_to_decimal(concatenate(10, 11, 101, ..., binary((n-2)th prime), binary((n-1)th prime), binary(n-th prime), binary((n-1)th prime), binary((n-2)th prime), ..., 101, 11, 10))

cp's OEIS Frontend

A138143 Triangle read by rows in which row n lists p(1), p(2), ..., p(n), p(n-1), ..., p(1), where p(i) = i-th prime.

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

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