Fwd: Most "compact" sequence such that there is at least one prime between a(n) and a(n+1)

[Maximilian Hasler]

"David W. Wilson" <wilson.d at anseri.com>:
> Also, the b-files for A005250 and A002386 need to be verified against one another.
> They should be of the same length, and I'm not sure the primes and gaps listed in them match up.

Well they don't need to be of same length (different sources are quoted), but
indeed the entry #68 (last term of A002386) seems to have a problem
for one of them:

A005250=readvec("A005250.dat");
A002386=readvec("A002386.dat");
vector(68,i,A002386[i]+A005250[i])
(08:41) gp > isprime(%)
%220 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
0]

(08:41) gp > [A002386[68],A005250[68],A002386[68]+A005250[68]]
%222 = [218034721194214273, 1224, 218034721194215497]
(08:46) gp > isprime(%)
%223 = [1, 0, 0] \\ should be [1,*,1]

M.H.
PS: below all values

A005250=readvec("A005250.dat")
%221 = [1, 2, 4, 6, 8, 14, 18, 20, 22, 34, 36, 44, 52, 72, 86, 96,
112, 114, 118, 132, 148, 154, 180, 210, 220, 222, 234, 248, 250, 282,
288, 292, 320, 336, 354, 382, 384, 394, 456, 464, 468, 474, 486, 490,
500, 514, 516, 532, 534, 540, 582, 588, 602, 652, 674, 716, 766, 778,
804, 806, 906, 916, 924, 1132, 1184, 1198, 1220, 1224, 1248, 1272,
1328, 1356, 1370, 1442]

A002386=readvec("A002386.dat")
%217 = [2, 3, 7, 23, 89, 113, 523, 887, 1129, 1327, 9551, 15683,
19609, 31397, 155921, 360653, 370261, 492113, 1349533, 1357201,
2010733, 4652353, 17051707, 20831323, 47326693, 122164747, 189695659,
191912783, 387096133, 436273009, 1294268491, 1453168141, 2300942549,
3842610773, 4302407359, 10726904659, 20678048297, 22367084959,
25056082087, 42652618343, 127976334671, 182226896239, 241160624143,
297501075799, 303371455241, 304599508537, 416608695821, 461690510011,
614487453523, 738832927927, 1346294310749, 1408695493609,
1968188556461, 2614941710599, 7177162611713, 13829048559701,
19581334192423, 42842283925351, 90874329411493, 171231342420521,
218209405436543, 1189459969825483, 1686994940955803, 1693182318746371,
43841547845541059, 55350776431903243, 80873624627234849,
218034721194214273]

(08:40) gp > diff=vector(68,i,A002386[i]+A005250[i])
%219 = [3, 5, 11, 29, 97, 127, 541, 907, 1151, 1361, 9587, 15727,
19661, 31469, 156007, 360749, 370373, 492227, 1349651, 1357333,
2010881, 4652507, 17051887, 20831533, 47326913, 122164969, 189695893,
191913031, 387096383, 436273291, 1294268779, 1453168433, 2300942869,
3842611109, 4302407713, 10726905041, 20678048681, 22367085353,
25056082543, 42652618807, 127976335139, 182226896713, 241160624629,
297501076289, 303371455741, 304599509051, 416608696337, 461690510543,
614487454057, 738832928467, 1346294311331, 1408695494197,
1968188557063, 2614941711251, 7177162612387, 13829048560417,
19581334193189, 42842283926129, 90874329412297, 171231342421327,
218209405437449, 1189459969826399, 1686994940956727, 1693182318747503,
43841547845542243, 55350776431904441, 80873624627236069,
218034721194215497]