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
A102501
Primes of the concatenated form 7nn7.
Original entry on oeis.org
715157, 718187, 719197, 734347, 736367, 739397, 748487, 752527, 757577, 760607, 767677, 775757, 779797, 781817, 785857, 796967, 797977, 7100510057, 7102010207, 7103010307, 7104710477, 7105410547, 7106210627, 7106510657, 7107410747
Offset: 1
Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 13 2005
715157 is prime and of the form 7nn7 for n=15.
7100510057 is prime and of the form 7nn7 for n=1005.
Cf.
A102897 for sequence of all numbers of form 7nn7.
A102500 for the n values corresponding to the primes in this sequence.
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Select[Table[FromDigits[Join[{7},IntegerDigits[n],IntegerDigits[n],{7}]],{n,1100}],PrimeQ] (* Harvey P. Dale, Jun 05 2024 *)
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.