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

[Maximilian Hasler]

If we take as new version of A002386 the prevprime() of A000101 (73 terms),
we get exactly the gaps from A005250, except for the last term #74 of
that seq., corresponding to a gap starting at 804212830686677669
according to Andersen's web page. (This is almost twice the preceding
value, but I take Andersen's data for granted.)
Adding that one to A002386_new and taking A000101_new = nextprime(%)
we get exactly A005250 as difference.
Below the values, I'll send b-files to Neil.
Maximilian


 gp > A002386_new=vector(#A000101,i,precprime(A000101[i]-1));
 gp > A002386_new=concat(A002386_new,804212830686677669)
%241 = [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,
203986478517455989, 218034721194214273, 305405826521087869,
352521223451364323, 401429925999153707, 418032645936712127,
804212830686677669]
 gp > #%
%242 = 74
 gp > A000101_new=vector(#A002386_new,i,nextprime(A002386_new[i]+1))
%243 = [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,
203986478517457213, 218034721194215521, 305405826521089141,
352521223451365651, 401429925999155063, 418032645936713497,
804212830686679111]
 gp > A005250_new=A000101_new-A002386_new
%244 = [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]
 gp > #%
%245 = 74
 gp > A005250
%246 = [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]