A089824 -id:A089824 - cp's OEIS frontend

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

Zak Seidov, Mar 06 2009

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

			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).

Donovan Johnson, Table of n, a(n) for n=1..345
Carlos Rivera, Puzzle 163. P+SOD(P), The Prime Puzzles and Problems Connection.

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.

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

A157655 Zeroless primes p such that the next prime after p can be obtained from p by adding the sum and product of the digits of p.

Original entry on oeis.org

11411, 16111, 1112113, 1151113, 14161111, 14611111, 111115141, 111253111, 115112113, 122112311, 151151111, 211711111, 1111116211, 1121123111, 1121181311, 1211215111, 1412113111, 1416131111, 2111121511, 2111215111

Offset: 1

Cino Hilliard, Mar 03 2009

If we allow a zero digit in p, we generate A089824. One could conjecture that the digit 1 must always appear in the entries of this sequence. The idea for this sequence and the description was motivated by A089823.

			The digits of 11411 add up to 8. The product of the digits is 4. So 11411+8+4 = 11423, the next prime after 11411. So 11411 is in the sequence.

Cino Hilliard, Pointer primes [broken link]

Cf. A089823, A089824.

zpQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&NextPrime[n] == n+ Total[ idn]+Times@@idn]; Select[Prime[Range[11*10^7]],zpQ] (* Harvey P. Dale, Jan 14 2016 *)

cp's OEIS Frontend

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

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