This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A368735 #31 Feb 19 2025 12:11:47
%S A368735 -1,-1,1,-1,2,-1,-1,4,3,-1,-1,6,-1,5,-1,-1,-1,-1,9,7,-1,-1,12,8,14,-1,
%T A368735 11,-1,-1,16,-1,-1,26,49,-1,-1,-1,40,-1,20,-1,51,-1,23,-1,-1,30,24,81,
%U A368735 124,27,15,-1,29,-1,-1,-1,-1,54,-1,44,-1,39,169,31,-1
%N A368735 Table read by ascending antidiagonals: A(n,m) is the smallest number k such that k and k+1 have the n-th and m-th prime signatures, respectively, or -1 if no such k exists.
%F A368735 A(n,m) = min_{ k : A046523(k) = A025487(n) AND A046523(k+1) = A025487(m) }, or -1 if no such k exists.
%e A368735 A(6,10) = 242 because 242 is the smallest number k of the form p^2 * q (the 6th prime signature; see A025487) such that k+1 is of the form r^5 (the 10th prime signature): 242 = 2 * 11^2 and 243 = 3^5.
%e A368735 A(2,7) = -1 because there exists no number k such that k is a prime (the 2nd prime signature) and k+1 is the fourth power of a prime (the 7th prime signature). (If k+1 = q^4 for some prime q, then k = (q-1)*(q+1)*(q^2+1), which cannot be a prime.)
%e A368735 The table below gives additional terms.
%e A368735 .
%e A368735 n\m| 1 2 3 4 5 6 7 8 9 10 11 12
%e A368735 ---+-------------------------------------------------------------------
%e A368735 1 | -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
%e A368735 2 | -1 2 3 5 7 11 -1 23 29 31 -1 47
%e A368735 3 | -1 4 -1 9 -1 49 -1 -1 169 -1 -1 57121
%e A368735 4 | -1 6 -1 14 26 51 15 39 65 -1 35 111
%e A368735 5 | -1 -1 8 -1 -1 27 -1 343 2197 -1 -1 -1
%e A368735 6 | -1 12 -1 20 124 44 -1 188 153 242 99 175
%e A368735 7 | -1 16 -1 81 -1 -1 -1 -1 130321 -1 -1 -1
%e A368735 8 | -1 40 24 54 -1 152 -1 135 104 -1 -1 1647
%e A368735 9 | -1 30 -1 105 205378 170 -1 231 230 16806 195 890
%e A368735 10 | -1 -1 -1 32 -1 243 -1 -1 3125 -1 -1 -1
%e A368735 11 | -1 36 -1 225 -1 1444 -1 69189124 441 -1 -1 96393124
%e A368735 12 | -1 112 48 176 4912 368 80 567 272 1419856 6723 2511
%Y A368735 Cf. A025487, A046523, A343144.
%K A368735 sign,tabl
%O A368735 1,5
%A A368735 _Jon E. Schoenfield_, Jan 04 2024