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A258437 Smallest number m such that A062234(m) = A062234(m-1+k) for k = 1..n.

%I A258437 #22 Oct 08 2022 00:01:46
%S A258437 9,1,302,332,465460,67928439
%N A258437 Smallest number m such that A062234(m) = A062234(m-1+k) for k = 1..n.
%C A258437 From _Michel Marcus_, Feb 09 2022: (Start)
%C A258437 Previous name: "Smallest number m such that A258383(m) = n" was not ok. For instance, for a(1) the smallest m such that A258383(m)=1 is 5, then we have to sum up the first 5 terms 2+2+2+2+1 to get 9, as shown in the example table (whose 2nd and 3rd column names I edited too).
%C A258437 Note that prime([302, 332, 465460]) = [1997, 2237, 6824897] which is a subsequence of A090807. Then one can verify that primepi(1356705137 = A090807(7)) = 67928439 and primepi(3637803390827 = A090807(8)) = 130463972798 are good candidates for a(6) and a(7). a(6) has been confirmed by program. (End)
%F A258437 A258383(a(n)) = n and A258383(m) != n for m < a(n);
%F A258437 let m = A258432(a(n)): A062234(m) = A062234(m-1+k) for k = 1..n.
%e A258437    n |   f(n) | a(n) = A258432(f(n)) |     Run in A062234
%e A258437   ---+--------+----------------------+--------------------------
%e A258437    1 |      5 |       9 = A258469(1) | [17]
%e A258437    2 |      1 |       1 = A257762(1) | [1, 1]
%e A258437    3 |    265 |     302 = A258449(1) | [1995, 1995, 1995]
%e A258437    4 |    290 |     332 = A257892(1) | [2235, 2235, 2235, 2235]
%e A258437    5 | 440676 |  465460 = A257951(1) | [ ___ 5 x 6824895 ___ ]
%o A258437 (Haskell)
%o A258437 import Data.List (elemIndex); import Data.Maybe (fromJust)
%o A258437 a258437 = (+ 1) . fromJust . (`elemIndex` a258383_list)
%o A258437 (PARI) f(n) = 2*prime(n) - prime(n+1); \\ A062234
%o A258437 lista(nn) = {my(vp=primes(nn)); my(v=vector(nn-1, k, 2*vp[k] - vp[k+1]), last=v[1], nb=1, list=List()); kill(vp); for (n=2, nn-1, if (v[n]==last, nb++, listput(list, nb); last=v[n]; nb=1);); Vec(list);} \\ A258383
%o A258437 find(k, v) = {my(i=1); while (v[i] != k, i++); i;}
%o A258437 listr(nn) = {my(v=lista(nn)); for (k=1, 6, my(pos = find(k, v)); print1(sum(i=1, pos, v[i])- k + 1, ", "););}
%o A258437 listr(9*10^7) \\ _Michel Marcus_, Feb 09 2022
%Y A258437 Cf. A062234, A258383, A258432, A258469, A257762, A258449, A257892, A257951.
%Y A258437 Cf. A090807.
%K A258437 nonn,more
%O A258437 1,1
%A A258437 _Reinhard Zumkeller_, May 31 2015
%E A258437 New name and a(6) from _Michel Marcus_, Feb 09 2022