A089323 -id:A089323 - cp's OEIS frontend

A100986 Smallest k such that concatenation of rk and 1 is a prime for all r = 1 to n but not prime for r = n+1, or smallest k such that 10r*k+1 is a prime for all r = 1 to n but not prime for r = n+1.

1, 3, 21, 33, 1083, 2541, 822486, 51282, 1296060612

Offset: 1

Ray G. Opao, Jan 13 2005

a(10) > 10^10. - Robert Price, Apr 02 2019

			a(4)=33 because 331, 661, 991 and 1321 (1321=10*4*33+1) are all prime, but 1651 (1651=10*5*33+1) is not prime. - _Robert Price_, Apr 02 2019

Cf. A089323.

Table[k = 1;
While[! AllTrue[Table[10*r*k + 1, {r, 1, n}], PrimeQ] ||
PrimeQ[10*(n + 1)*k + 1], k++]; k, {n, 1, 9}] (* Robert Price, Apr 02 2019 *)

isok(k, n) = {for (r=1, n, if (! isprime(10*r*k+1), return (0));); !isprime(10*(n+1)*k+1);}
a(n) = {my(k=1); while(! isok(k, n), k++); k;} \\ Michel Marcus, Apr 03 2019

Corrected a(7) and added a(9) by Robert Price, Apr 02 2019

A090180 Primes p = prime(n) such that p + sum-of-digits(p) +- 1 = prime(n+1).

Original entry on oeis.org

2, 3, 23, 61, 131, 151, 331, 601, 661, 1013, 1033, 1103, 1123, 1231, 1237, 1259, 1307, 1321, 1811, 2131, 2621, 2861, 3301, 4021, 4159, 4373, 4463, 4733, 4759, 4801, 5059, 5101, 6151, 6229, 6397, 6737, 7079, 7369, 7433, 8191, 9109, 10181, 10691, 11119

Offset: 1

Enoch Haga, Jan 19 2004

			a(2)=23. S(d)=5. 23+5=28. 28+1=29, the next prime in sequence. a(3)=61. S(d)=7. 61+7=68. 68-1=67, the next prime in sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A089323.

ppQ[n_]:=Module[{sidn=Total[IntegerDigits[n[[1]]]]},n[[1]]+sidn+1 == n[[2]]||n[[1]]+sidn-1==n[[2]]]; Transpose[Select[Partition[Prime[ Range[1500]],2,1],ppQ]][[1]] (* Harvey P. Dale, Mar 19 2012 *)

cp's OEIS Frontend

A100986 Smallest k such that concatenation of rk and 1 is a prime for all r = 1 to n but not prime for r = n+1, or smallest k such that 10r*k+1 is a prime for all r = 1 to n but not prime for r = n+1.

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A090180 Primes p = prime(n) such that p + sum-of-digits(p) +- 1 = prime(n+1).

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Author

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Programs

Mathematica

cp's OEIS Frontend

A100986 Smallest k such that concatenation of r*k and 1 is a prime for all r = 1 to n but not prime for r = n+1, or smallest k such that 10*r*k+1 is a prime for all r = 1 to n but not prime for r = n+1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions

A090180 Primes p = prime(n) such that p + sum-of-digits(p) +- 1 = prime(n+1).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A100986 Smallest k such that concatenation of rk and 1 is a prime for all r = 1 to n but not prime for r = n+1, or smallest k such that 10r*k+1 is a prime for all r = 1 to n but not prime for r = n+1.