A152606 a(1) = 1; thereafter a(n) is always the smallest integer > a(n-1) not leading to a contradiction, such that any six consecutive digits in the sequence sum up to a prime.

1, 2, 3, 4, 5, 8, 9, 21, 45, 83, 89, 450, 503, 630, 701, 810, 901, 2101, 2103, 4121, 6301, 6303, 6503, 6901, 43030, 70103, 81010, 90101, 210101, 210103, 210107, 210109, 210143, 210145, 210149, 210161, 210163, 210167, 210169, 210503

Offset: 1

Author

N. J. A. Sloane, Sep 23 2009

Keywords

• nonn
• base

Comments

Computed by Jean-Marc Falcoz.

From a(269) = 1010001010 on, there starts a pattern of 104 terms, which then repeats indefinitely (with 6 digits in the middle of each term duplicated). - M. F. Hasler, Oct 16 2009

Links

• Eric Angelini, Chiffres consecutifs dans quelques suites
• E. Angelini, Chiffres consecutifs dans quelques suites [Cached copy, with permission]

Crossrefs

Cf. A158652, A152604, A152605, A152607, A152608, A152609.

Programs

PARI

a(n, show_all=0, s=[1, 2, 3, 4, 5, 8, 9, 21, 45, 83, 89, 450, 503, 630, 701, 810, 901, 2101, 2103, 4121, 6301, 6303, 6503, 6901, 43030])={ my(a,nd=#Str(s[ #s])); for(i=1,n, if( i<=#s, a=s[i], my(ld=a%10^nd); while(a++,my(t=a+ld*10^#Str(a));forstep(d=#Str(a)-1,0,-1,isprime(sum(j=d,d+nd,t\10^j%10))&next;a+=10^d-a%10^d-1; next(2));break));show_all & print1(a", "));a} \\ M. F. Hasler, Oct 16 2009