A157789 Primes p such that consecutive primes p < q < r < s all are additive pointer-primes A089824.

317130731, 521142283, 557010073, 1000702693, 1281321101, 1613435111, 1802692181, 2010808001, 2012656781, 2238160121, 2352422231, 3361114331, 4302122501, 4902109481, 5044120093, 6276507313, 6542906413, 7230842923

Offset

1,1

Comments

We may call these primes the additive pointer-primes of 4th order (and then A089824 are additive pointer-primes of first order).

Are there additive pointer-primes of higher than 4th order?

The only known 5th-order additive pointer-prime < 10^12 is 102342031273 (Donovan Johnson, Oct 25 2009).

The first 10 5th-order additive pointer-primes are 102342031273, 1012835563819, 1070302300183, 2350811300953, 3063433129909, 3104103122173, 3551303300933, 5262316326901, 5426670290957, 6104611400971. The first 6th-order additive pointer-prime is 63604045061911. - Giovanni Resta, Jan 14 2013

Links

Donovan Johnson, Table of n, a(n) for n=1..345

Carlos Rivera, Puzzle 163. P+SOD(P), The Prime Puzzles and Problems Connection.

Example

p=317130731, q=317130757, r=317130791, s=317130823, t=317130851;
p + sod (p) = q, q + sod (q) = r, r + sod (q) = s, s + sod (s) =t;
p<q<r<s<t are consecutive primes, sod(m)=A007953(m).

Crossrefs

Cf. A007953 Digital sum (i.e., sum of digits) of m, A089824 Primes p such that the next prime after p can be obtained from p by adding the sum of the digits of p.

Sequence in context: A221985 A219784 A105005 * A331445 A331446 A184573

Adjacent sequences: A157786 A157787 A157788 * A157790 A157791 A157792

Keyword

base,nonn

Author

Zak Seidov, Mar 06 2009

Extensions

a(13)-a(18) from Donovan Johnson, Oct 11 2009

Status

approved