A381120 Numbers k such that both A381019(k) and A381019(k+1) are composite.

63, 630, 2423, 5653, 9104, 26308, 36108, 41622, 64526, 85121, 108917, 143913, 148305, 176405, 316974, 399168, 399907, 406487, 536926, 621016, 830793, 937038, 937109, 970243, 1088629, 1480545, 1895503, 3961587, 4651102, 5171081, 5487450, 6219705, 7327856, 8118740

Offset: 1

Author

N. J. A. Sloane, Feb 15 2025

Keywords

• nonn

Comments

Initially, A381019 consists of runs of primes separated by single composite numbers. These indices k mark the beginning of two or more consecutive composite numbers in A381019.

Crossrefs

Cf. A381019, A379810 (the values of A381019(k)).

Programs

PARI

lista(nn) = my(c, f, m=1, q=1, r=0, t, u=List([]), w=vector(nn)); for(n=2, nn, t=0; forprime(p=2, max(m, sqrtint(n)), c=n-1-w[p]; if(c>1&&!w[c], listput(u, c))); listsort(u, 1); for(i=1, #u, c=u[i]; f=factor(c)[, 1]; t=1; for(j=1, #f, if(n-c<=w[f[j]], t=0; break)); if(t, u=u[i+1..#u]; if(r, print1(n-1, ", ")); r=1; w[c]=1; for(j=1, #f, w[f[j]]=n); m=max(m, f[#f]); break)); if(!t, r=0; u=List([]); if(nn>q=nextprime(q+1), w[q]=n))); \\ Jinyuan Wang, Feb 16 2025

Extensions

a(7)-a(8) from Michael De Vlieger, Feb 15 2025

a(9)-a(34) from Jinyuan Wang, Feb 16 2025