A102497 -id:A102497 - cp's OEIS frontend

A100846 Concatenate (1,n,n,1).

1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 110101, 111111, 112121, 113131, 114141, 115151, 116161, 117171, 118181, 119191, 120201, 121211, 122221, 123231, 124241, 125251, 126261, 127271, 128281, 129291, 130301, 131311, 132321

Offset: 0

Parthasarathy Nambi, Jan 07 2005

			For n = 0, concatenate(1,n,n,1) is 1001 = a(0).
For n = 5, concatenate(1,n,n,1) is 1551 = a(5).
For n = 10, concatenate(1,n,n,1) is 110101 = a(10).

M. F. Hasler, Table of n, a(n) for n = 0..10000 (Terms a(1..9999) from Robert Israel)

Cf. A100896 (3nn3), 7nn7 (A100897), 9nn9 (A102484).

For primes in these sequences: A102496, A102497 (1nn1); A102498, A102499 (3nn3); A102500, A102501 (7nn7); A102502, A102503 (9nn9); A102504 (intersection).

seq(seq((10^(2*d+1)+1+(10^(d+1)+10)*n), n=`if`(d>1,10^(d-1),0) .. 10^d-1),d=1..3);
# Robert Israel, Dec 30 2015, edited for n=0 by M. F. Hasler, Jun 25 2018

For[n = 0, n < 30, n++, l := Floor[Log[10, Min[n,1]] + 1]; gvout := (n*10^l + n)*10 + 1; m := Floor[Log[10, gvout]]; giveout := 10^(m + 1) + out; Print[giveout]] (* Stefan Steinerberger, Jan 27 2006, edited for n=0 by M. F. Hasler, Jun 25 2018 *)

A100846(n)=eval(Str(1,n,n,1)) \\ M. F. Hasler, Jun 22 2018

G.f.: 1001 + x*(31-11*x)/(1-x)^2 + Sum_{k>=0} 90*(12*10^(2*k)*(1-x)+10^k*x)*x^(10^k)/(1-x)^2. - Robert Israel, Dec 30 2015

More terms from Stefan Steinerberger, Jan 27 2006

Definition reworded and missing 1001 added by M. F. Hasler, Jun 22 2018

A102496 Values of n for which the concatenation of the form 1nn1 (sequence A100846) are primes.

Original entry on oeis.org

12, 13, 15, 19, 27, 31, 34, 36, 40, 42, 45, 49, 57, 58, 61, 69, 70, 72, 78, 82, 87, 90, 91, 96, 97, 1000, 1002, 1017, 1018, 1024, 1033, 1035, 1063, 1068, 1069, 1074, 1084, 1086, 1090, 1095, 1110, 1114, 1116, 1117, 1126, 1128, 1173, 1174, 1179, 1185, 1189, 1192

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 12 2005

All terms == 0 or 1 (mod 3), and have an even number of decimal digits. - Robert Israel, May 09 2017

			For n=12 we have 112121, which is prime.
For n=13 we have 113131, which is prime.
For n=1000 we have 1100010001, which is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A100846. The primes themselves are in sequence A102497.

f:= n -> 1 + 1*10^(2*ilog10(n)+3)+(n)*(10+10^(2+ilog10(n))):
select(n -> isprime(f(n)), [$1..2000]); # Robert Israel, May 09 2017

Select[Range@ 1200, PrimeQ[FromDigits@ Join[{1}, #, #, {1}]] &@ IntegerDigits[#] &] (* Michael De Vlieger, May 09 2017 *)

A102504 Values of n for which the concatenations 1nn1, 3nn3, 7nn7 and 9nn9 are all primes.

Original entry on oeis.org

2092, 2131, 2797, 3433, 4126, 5524, 5710, 6817, 8383, 8815, 9472, 114613, 116329, 130213, 206776, 239389, 282298, 286642, 306046, 307180, 311317, 318310, 341386, 360733, 366529, 377005, 425665, 430597, 460441, 475642, 475660, 478078, 490870

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 13 2005

			E.g. n=2092 leads to 1209220921, 3209220923, 7209220927 and 9209220929, all of which are primes.

For full sequences of integers of form 1nn1 (A100846), 3nn3 (A100896), 7nn7 (A100897), 9nn9 (A102484). For primes in these sequences: 1nn1 (A102496, A102497), 3nn3 (A102498, A102499), 7nn7 (A102500, A102501), 9nn9 (A102502, A102503).

foQ[n_, o_] := Block[{id = IntegerDigits[n]}, PrimeQ[ FromDigits[ Join[{o}, id, id, {o}] ]]]; Select[ Range[500985], foQ[ #, 1] && foQ[ #, 3] && foQ[ #, 7] && foQ[ #, 9] &] (* Robert G. Wilson v, Jan 14 2005 *)

cp's OEIS Frontend

A100846 Concatenate (1,n,n,1).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions

A102496 Values of n for which the concatenation of the form 1nn1 (sequence A100846) are primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

A102504 Values of n for which the concatenations 1nn1, 3nn3, 7nn7 and 9nn9 are all primes.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica