A099609 -id:A099609 - cp's OEIS frontend

A176831 List of all primes p such that 2*A099609(2n-1)A099609(2n).

5, 7, 11, 13, 23, 37, 59, 61, 83, 277, 359, 383, 397, 457, 479, 541, 563, 839, 863, 1201, 1237, 1283, 1319, 1321, 1619, 1621, 1657, 2039, 2063, 2099, 2459, 2557, 2579, 2857, 2903, 2963, 3217, 3863, 4057, 4177, 4259, 4261, 4283, 4621, 4679, 5099, 5101, 5581

Offset: 1

Juri-Stepan Gerasimov, Apr 27 2010

nonn

Where A099609 is a naive list of twin primes (A077800 prefixed by 2,3).

			a(1)=5 because 2*A099609(2*1-1)=4<5(prime)<2*A099609(2*1)=6;
a(2)=7 because 2*A099609(2*2-1)=6<7(prime)<2*A099609(2*2)=10;
a(3)=11 and a(4)=13 because 2*A099609(2*3-1)<11(prime)<13(prime)<2*A099609(2*3).

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A077800, A099609, A171821.

Flatten@ Map[Select[Range @@ #, PrimeQ] &, 2 Select[Partition[#, 2, 1] &@ Prime@ Range@ 410, First@ Differences@ # <= 2 &]] (* Michael De Vlieger, Mar 18 2017 *)

Entries checked by R. J. Mathar, May 10 2010

A176834 List of all primes p such that 3*A099609(2n-1)A099609(2n).

Original entry on oeis.org

7, 11, 13, 17, 19, 37, 53, 89, 127, 179, 181, 307, 449, 541, 577, 593, 683, 719, 809, 811, 937, 1259, 1297, 1567, 1709, 1801, 1979, 2467, 2647, 3061, 3187, 3457, 3691, 3833, 3907, 4283, 4357, 4447, 4463, 4861, 5003, 5167, 5849, 5851, 6247, 6263, 6337, 6389

Offset: 1

Juri-Stepan Gerasimov, Apr 27 2010

nonn

Where A099609 is a naive list of twin primes (A077800 prefixed by 2,3).

			a(1)=7 because 3*A099609(2*1-1)=6<7(prime)<3*A099609(2*1)=9; a(2)=11 and a(3)=13 because 3*A099609(2*2-1)=9<11(prime)<13(prime)<3*A099609(2*2)=15; a(4)=17 and a(5)=19 because 3*A099609(2*3-1)=15<17(prime)<19(prime)<3*A099609(2*3)=21.

Cf. A171821.

Contribution from R. J. Mathar, May 10 2010: (Start)
A077800 := proc(n) if type(n,'even') then A006512(n/2) ; else A001359((n+1)/2) ; end if; end proc:
A099609 := proc(n) if n <= 2 then n+1 ; else A077800(n-2) ; end if; end proc:
for n from 1 to 100 do lpr := 3*A099609(2*n-1) ; upr := 3*A099609(2*n) ; for p from lpr+1 to upr-1 do if isprime(p) then printf("%d,",p) ; end if; end do: end do: (End)

Corrected (3691 inserted) by R. J. Mathar, May 10 2010

A138329 List of strictly non-palindromic twin primes {p, p+2}.

Original entry on oeis.org

137, 139, 4337, 4339, 8291, 8293, 9419, 9421, 10937, 10939, 13757, 13759, 19427, 19429, 20981, 20983, 36011, 36013, 38327, 38329, 43397, 43399, 59441, 59443, 71327, 71329, 74717, 74719, 76871, 76873, 90437, 90439, 91571, 91573, 117239

Offset: 1

Karl Hovekamp, Mar 14 2008

The strictly non-palindromic twin primes are a part of the normal twin primes. See the list of twin primes A077800 and A016038 for the strictly non-palindromic numbers.

Karl Hovekamp, Palindromzahlen in adischen Zahlensystemen, 2004

K. Hovekamp, Palindromic numbers in different bases.
K. Hovekamp, Strictly non-palindromic prime twins up to 1 billion.
Wikipedia, Strictly non-palindromic numbers.

Cf. A016038, A047811, A016038, A077800, A099609.

Twin primes, where both numbers {p} and {p+2} are strictly non-palindromic.

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A176831 List of all primes p such that 2*A099609(2n-1)A099609(2n).

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A176834 List of all primes p such that 3*A099609(2n-1)A099609(2n).

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A138329 List of strictly non-palindromic twin primes {p, p+2}.

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