A100846
Concatenate (1,n,n,1).
Original entry on oeis.org
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
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).
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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
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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 *)
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A100846(n)=eval(Str(1,n,n,1)) \\ M. F. Hasler, Jun 22 2018
Definition reworded and missing 1001 added by
M. F. Hasler, Jun 22 2018
A102503
Primes of the concatenated form 9nn9.
Original entry on oeis.org
910109, 913139, 916169, 917179, 920209, 923239, 928289, 931319, 935359, 937379, 946469, 953539, 956569, 961619, 965659, 968689, 974749, 982829, 994949, 995959, 998989, 9101010109, 9101310139, 9101810189, 9104210429, 9104810489
Offset: 1
Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 13 2005
910109 is prime and of the form 9nn9 for n=10.
9101310139 is prime and of the form 9nn9 for n=1013.
Cf.
A102484 for sequence of all numbers of form 9nn9.
A102502 for the n values corresponding to the primes in this sequence.
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Select[Table[FromDigits[Join[{9},IntegerDigits[n],IntegerDigits[n],{9}]],{n,1100}],PrimeQ] (* Harvey P. Dale, Jul 28 2020 *)
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).
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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 *)
Showing 1-3 of 3 results.