A050674 -id:A050674 - cp's OEIS frontend

A133321 Inserting any (identical) digit between adjacent digits of an odd semiprime k never yields a prime.

15, 25, 35, 55, 65, 85, 95, 115, 121, 143, 145, 155, 185, 187, 205, 215, 235, 253, 265, 295, 299, 305, 335, 341, 355, 365, 393, 395, 411, 415, 437, 445, 451, 473, 485, 505, 515, 535, 545, 565, 583, 635, 655, 671, 679, 685, 695, 717, 745, 755, 781, 785, 815

Offset: 1

Jonathan Vos Post, Oct 18 2007

Odd semiprime analog of A050805. Trivially true for any digit if we substitute "even semiprime" for "odd semiprime." Trivially true for any semiprime which is a multiple of 5 (A001750). The nonmultiples of 5 in this sequence begin 121, 143, 187, 253, 299, 341.

			121 is in the sequence because 10201, 11211, 12221, 13231, 14241, 15251, 16261, 17271, 18281, 19291 are all composite.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001358, A001750, A050674-A050719, A050805, A050806.

Select[Select[Range[11,900,2],PrimeOmega[#]==2&],AllTrue[Table[ FromDigits[ Riffle[ IntegerDigits[#],n]],{n,0,9}],CompositeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 07 2018 *)

More terms from R. J. Mathar, Oct 22 2007

A050814 Primes p such that inserting any even digit between adjacent digits produces a prime number while inserting any odd digit produces a composite number, or vice versa.

Original entry on oeis.org

5333, 1454969, 1466833, 1790531, 1794343, 1883113, 1984459, 2179993, 2410523, 2567891, 3100301, 3259567, 3424783, 3700153, 3954131, 3972979, 4046671, 4134133, 4280033, 4544641, 4691851, 4692641, 4848523, 5006831, 5118307

Offset: 1

Patrick De Geest, Oct 15 1999

			5333 produces five primes when an even digit is inserted (5030303, 5232323, 5434343, 5636363, 5838383) and five composites when an odd digit is inserted (5131313, 5333333, 5535353, 5737373, 5939393).

Cf. A050674-A050719.

a[n_,k_]:=Union[Boole/@PrimeQ[Table[FromDigits[Riffle[IntegerDigits[n],i]],{i,k+2*Range[0,4]}]]]; t={}; Do[p=Prime[i]; x=a[p,1]; y=a[p,0]; If[x=={0}&&y=={1}||x=={1}&&y=={0},AppendTo[t,p]],{i,100,190000}]; t (* Jayanta Basu, Jun 01 2013 *)

Offset changed to 1 by Jon E. Schoenfield, Oct 17 2019

Name clarified by Tanya Khovanova, Jul 06 2021

cp's OEIS Frontend

A133321 Inserting any (identical) digit between adjacent digits of an odd semiprime k never yields a prime.

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