Product of two palindromic primes A002385

[Jonathan Post]

Leroy Quet's clever A143016 All terms are a palindrome (binary) makes
me suggest the obvious base 10 sequence (which might not pass the
summer rules threshhold but is so simple):

Product of two palindromic primes A002385.

4, 6, 9, 10, 14, 15, 21, 22, 25, 33, 35, 49, 55, 77, 121, 202, 262,
302, 303, 362, 382, 393, 453, 505, 543, 573, 626, 655, 706, 707, 746,
755, 766, 905, 917, 939, 955, 1057, 1059, 1111, 1119, 1149, 1267,
1337, 1441, 1454, 1514, 1565, 1574, 1594, 1661, 1765, 1838, 1858,
1865, 1915, 1991, 2101, 2181, 2191, 2271, 2361, 2391, 2471, 2611,
2681, 2757, 2787, 3443, 3635, 3785, 3883, 3935, 3985, 4103, 4213,
4595, 4645, 5089,  5299, 5509, 5579, 6433, 6503, 7997, 8327, 8657,
8767, 10109, 10201, 10219, 13231, 15251, 17161, 18281, 19291, 19781,
20602, 21002, 21202, 22622, 22801, 23711, 25021, 27331, 28841, 30903,
31613, 32761, 34571, 36481, ..., 5653?, ..., 37673, 41003, 46243,
47263, 48863, 50173, 51505, 53303, 56323, 56653, 57833, 59783, 63893,
67423, 67513, 69323, 71243, 72107, 73153, 73427, 76457, 79487, 80497,
92819, 93829, 95237, 97969, 99167, 103097, 104407, 109777, 110489,
113311, 114307, 116749, 118837, 119879, 120347, 120389, 121699,
124609,  131587, 131669, 1349431, 135199, 137017, 138769, 138857,
139129, 140279, 142447, 142859, 144257, 144587, 146689, 150317,
152227, 166339, 168149, 175529, 177439, 227551, 236941, 246331,
249461, 256631, 267221, 271171, 277811, 278441, 281341, 282361,
287647, 289931, 290777, 293551, 297281, 301421, 305251, 324407,
327937, 342787, 346517, 351977, 355807, 528529, 550339, ..., 1555451,
572149, 573049, 579419, 595759, 603329, 619369, 627239, 635209,
668113, 675383, 695683, 703253, 723253, 731123, 732443, 740413,
844561, 853751, 863041, ..., 1864481, 1967491, ..., 1040401, ...

nonn, base, easy,

Subset of my A140332 Products of two palindromes in base 10.

A001358 INTERSECTION A140332.

Cf. A116993  a(n) is the least number having exactly n representations
as a product of two palindromes.

Consecutive number pairs in this set begin:
{(9,10), (14,15), (21,22), (302, 303), (706, 707), ...).

The subset of these that are themselves palindromes begins: {4, 6, 9,
22, 33, 55, 77, 121, 202, 303, 505, 707, 1441, 1661, 1991, 3443, 3883,
7997, 10201, 13231, 15251, 18281, 19291, 31613, 35653, 37673, 38683,
..., 113311, ..., 1040401, ...}.

Sorry for my cut-and paste error which lost a term ..., 5653?, ...

Best,

Jonathan Vos Post



Last year I submitted a ten-thousand value "b-file" for A036236. The  
link to it says only one-thousand: that can be fixed.

I was going to offer a similar ten-thousand value "b-file" for  
A078457, but I just noticed that Jan-Christoph Schlage-Puchta has  
contributed a one-thousand value file only two months ago that betters  
my attempt by going as high as 418943222963 (for the number 784,  
though not as high as 622699582951 - Joe Crump's conjectured a(34)).  
As with last year's file, I only checked up to 10^11, so I'll hold  
onto my bigger, but not better file.

Why is a(0) = 3, and not 1?

Hans