Error-finding program

[franktaw at netscape.net]

(See comments inline.)

Franklin T. Adams-Watters


-----Original Message-----
From: djr at nk.ca
...
    ... are probably monotonic-and-wrong:
A004993 wrong; 2 should be with next term
A005620 certainly wrong
A022041 a typo; the 212542 should be 7212542.
A037140 a typo: 241157564 should be 24157564.
A037458 definitely should be 16 instead of 1,6.
A052396 a typo: 3554432 should be 33554432
A056267 2684,19060 should be 268419060
A056514 2,200 should be 2200
A057886 definitely wrong; discussed here recently
A060774 certainly monotonic; probably 11,56987728 should be 1156987728
A061672 typo; 111111112222 should be 1111111112222.
A063040 this is correct; a(13) < a(12)
A067057 certainly monotonic; probably 53,903360 should be 53903360
A072561 4,8 should be 48
A072810 typo, 1700694 should be 170694
A113174 16737092 should be 16737092549

I don't know about A026001 A052468 A085611.

    ... are suspicious:
A007769 It looks like terms were added here that belong with an 
entirely different sequence.  I don't know if this is a computational 
error in the original sequence, the addition, or possibly the terms 
were added to the wrong sequence.

A026013 First, the g.f. is wrong - instead of (1 + x^2...), it should 
be (x + x^2...).  The last term, 5422121393500, should instead be 
54221213973500.

A026127 Should certainly be monotonic; I don't know what the correct 
value of a(19) is.
A026299 Should certainly be monotonic; I don't know what the correct 
value of a(11) is.
A026302 Should certainly be monotonic; I don't know what the correct 
value of a(18) is.
A026307 Should certainly be monotonic; I don't know what the correct 
value of a(31) is.
If Clark Kimberling is reading this, the last 4 sequences are yours; 
can you find your notes or program, and make the corrections?

A030278 Should be monotonic; I don't know what a(14) should be.

A054499 Similar to A007769, discussed above.
A064571 Should be monotonic; I don't know what a(10) should be.
A074030 3355432 should be 33554432.
A074352 I'm almost certain that the 9,41780 should be 941780.
A082674 A082675 I'm not certain, but these are probably correct.
A087525 I'm almost certain that the 3,7 should be 37.  (This sequence 
could use a better description.)

A088460 a(20) should probably be 14561 instead of 4561.  14561 is at 
least a twin prime.  (This sequence also contains a conjecture that is 
trivial: all twin primes except 3,5 are of the form 6n-1,6n+1; so as 
long as 3 is involved, the difference between any two lower twin primes 
is divisible by 6.)

A114497 A114498 These are probably correct; the ratios look OK.
A117504 There's something seriously wrong here, but I don't know just 
what.
A117988 Probably correct.  Prime values are generally lower than for 
non-primes; departure from monotonicity is not surprising.
A118058 4037743240 should be 40377, 43240
A121331 Looks like first row is repeated.
A122718 Is correct - note the abs in the definition.

I don't know about A005467 A051526 A051550 A055918 A097926 A100545 
A101234 A119626 A121210.

    ... have surprising trailing zeroes:
A026468 A026469 A026470 A030755 A030795 A037533 A037534 A048060 A048070
A049681 A054114

... which clearly do not belong for any of these.

    ... have STU/VWX mismatches:
A120002 A121049

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